R/jamesFunctions.R
In kristynpantoja/statexams: What the Package Does (One Line, Title Case)
generate_probability_rules = function(special = NULL){
if(special == 2){
tenths = seq(0.1, 0.8, 0.1)
prob_a = sample(tenths, 1)
prob_a_un_b = sample(seq(prob_a, 0.9, 0.1))
prob_b = prob_a_un_b - prob_a
prob_a_int_b = 0
return(c(prob_a, prob_b, prob_a_int_b, prob_a_un_b))
}
tenths = seq(0.2, 0.9, 0.1)
prob_a = sample(tenths, 1)
prob_b = sample(tenths, 1)
if(special == 1){
prob_a_int_b = prob_a * prob_b
}
else{
check = 0
while(check < 1.5){ #makes sure rounding doesn't give a bad value and events are dependent
check = 0
prob_a_int_b = round(runif(1, max(0.01, prob_a + prob_b - 1), min(prob_a, prob_b)), digits = 2)
if(prob_a_int_b != prob_a * prob_b){
check = check + 1
}
if(prob_a_int_b >= max(0.01, prob_a + prob_b - 1) & prob_a_int_b < min(prob_a, prob_b)){
check = check + 1
}
}
}
prob_a_un_b = prob_a + prob_b - prob_a_int_b
return(c(prob_a, prob_b, prob_a_int_b, prob_a_un_b))
}
#' Generate probability question
#'
#' @param type Determines the type of probability question. Valid inputs: 1, 2, 3
#'
#' @return a vector with first element as question, second element as correct answer, and other elements as other answer choices.
#' @export
#'
#' @examples makeQA_EventProbability(type = 1)
#' "Events A and B are independent.The probability of A is 0.9. The probability of B is 0.3. What is the probability that neither A nor B will occur?"
#' "0.070"
#' "0.600"
#' "0.270"
#' "1.200"
#' "0.930"
makeQA_EventProbability = function(type = NULL){
#type = 1 gives independence. 2 gives no assumptions. 3 gives mutually exclusive
if(is.null(type)){
type = sample(1:2,1)
}
if(type == 1){
checkques = 0
type.2 = sample(1:3, 1)
if(type.2 == 1){
while(checkques == 0){
probs = generate_probability_rules(1)
question = paste("Events A and B are independent.The probability of A is ", probs[1],
". The probability of B is ", probs[2], ". What is the probability of A intersection B?", sep = "")
ans1 = round(probs[3],3)
ans2 = round(abs(probs[1] - probs[2]),3)
ans3 = round(probs[4],3)
ans4 = round(probs[1] + probs[2],3)
ans5 = round(1 - probs[4],3)
answers = c(ans1, ans2, ans3, ans4, ans5)
if(length(unique(answers)) == 5){
checkques = 1
}
}
return(c(question, answers))
}
if(type.2 ==2){
while(checkques == 0){
probs = generate_probability_rules(1)
question = paste("Events A and B are independent.The probability of A is ", probs[1],
". The probability of B is ", probs[2], ". What is the probability of at least A or B occurring?", sep = "")
ans1 = round(probs[4],3)
ans2 = round(abs(probs[1] - probs[2]),3)
ans3 = round(probs[3],3)
ans4 = round(probs[1] + probs[2],3)
ans5 = round(1 - probs[4],3)
answers = c(ans1, ans2, ans3, ans4, ans5)
if(length(unique(answers)) == 5){
checkques = 1
}
}
return(c(question, answers))
}
if(type.2 ==3){
while(checkques == 0){
probs = generate_probability_rules(1)
question = paste("Events A and B are independent.The probability of A is ", probs[1],
". The probability of B is ", probs[2], ". What is the probability that neither A nor B will occur?", sep = "")
ans1 = round(1 - probs[4], 3)
ans2 = round(abs(probs[1] - probs[2]), 3)
ans3 = round(probs[3], 3)
ans4 = round(probs[1] + probs[2], 3)
ans5 = round(probs[4], 3)
answers = c(ans1, ans2, ans3, ans4, ans5)
if(length(unique(answers)) == 5){
checkques = 1
}
}
return(c(question, answers))
}
}
if(type == 2){
checkques = 0
while(checkques == 0){
probs = generate_probability_rules(0)
question = paste("The probability of A is ", probs[1],
". The probability of B is ", probs[2],
". The probability of A and B both occurring is ", probs[3],
". What is the probability of A or B occurring?", sep = "")
ans1 = round(probs[4],3)
ans2 = round(abs(probs[1] - probs[2]),3)
ans3 = round(probs[3],3)
ans4 = round(probs[1] + probs[2],3)
ans5 = round(1 - probs[4],3)
answers = c(ans1, ans2, ans3, ans4, ans5)
if(length(unique(answers)) == 5){
checkques = 1
}
}
return(c(question, answers))
}
if(type == 3){
checkques = 0
while(checkques == 0){
probs = generate_probability_rules(2)
question = paste("The probability of A is ", probs[1],
". The probability of B is ", probs[2],
". A and B are mutually exclusive. What is the probability of either A or B occurring?", sep = "")
ans1 = probs[1] + probs[2]
ans2 = abs(probs[1] - probs[2])
ans3 = probs[3]
ans4 = probs[4]
ans5 = 1 - probs[4]
answers = c(ans1, ans2, ans3, ans4, ans5)
if(length(unique(answers)) == 5){
checkques = 1
}
}
return(c(question, answers))
}
}
#' Generate expected value function
#'
#' @param prob Vector of probabilities corresponding to values vector. Must sum to 1 and be non-negative
#' @param values Vector of values that r.v. X takes
#'
#' @return a vector with first element as question, second element as correct answer, and other elements as other answer choices.
#' @export
#'
#' @examples makeQA_ExpectedValue(prob = c(0.4, 0.2, 0.4), values = c(2,4,8))
#' "f(2) = 0.4. f(4) = 0.2. f(8) = 0.4. What is the expected value of X?"
#' "4.8"
#' "14"
#' "15"
#' "84.672"
#' "5"
makeQA_ExpectedValue = function(prob = NULL, values = NULL){
if(is.null(prob) & is.null(values)){
n = sample(3:5, 1)
}
else if(is.null(prob) | is.null(values)){
n1 = length(prob)
n2 = length(values)
n = n1 + n2
}
else{
if(length(prob) != length(values)){
stop("prob and values lengths do not agree")
}
n = length(prob)
}
if(!is.null(prob) & sum(prob) != 1){
stop("prob must sum to 1 or be null")
}
if(!is.null(prob) & (sum(prob < 0) != 0)){
stop("prob must be positive")
}
if(is.null(values)){
values = sample(1:20, n)
values = sort(values)
}
if(is.null(prob)){
checkques = 0
while(checkques == 0){
prob = rep(0, n)
sticks = sample((25:90)/100, n-1 , replace = T)
remainprob = 100
for(i in 1:(n-1)){
prob[i] = floor(remainprob * sticks[i])
remainprob = remainprob - prob[i]
}
prob[n] = remainprob
prob = prob/100
question = ""
for(i in 1:n){
question = paste(question, "f(", values[i], ") = ", prob[i], ". ", sep = "")
}
question = paste(question, "What is the expected value of X?", sep = "")
ans1 = round(sum(values * prob), 3)
ans2 = round(sum(values), 3)
ans3 = round(sum(values + prob), 3)
ans4 = round(prod(values + prob), 3)
ans5 = round(mean(values))
answers = c(ans1, ans2, ans3, ans4, ans5)
if(length(unique(answers)) == 5){
checkques = 1
}
}
return(c(question,answers))
}
else{
question = ""
for(i in 1:n){
question = paste(question, "f(", values[i], ") = ", prob[i], ". ", sep = "")
}
question = paste(question, "What is the expected value of X?", sep = "")
ans1 = round(sum(values * prob), 3) #right
ans2 = round(sum(values), 3) #only summing the values
ans3 = round(sum(values + prob), 3) #adding values and prob
ans4 = round(prod(values + prob), 3) #product of (values + prob)
ans5 = round(mean(values)) #ignores probability and treats like sample mean
answers = c(ans1, ans2, ans3, ans4, ans5)
return(c(question,answers))
}
}
#' Generate hypothesis test question
#'
#' @param type Type of test 0: Left tail, 1: Right tail, 2: Two tailed
#' @param level Level of test. Must be great than 0 and less than 0.5
#' @param Xbar Sample mean
#' @param sigma Sample standard deviation
#' @param n Sample size
#' @param mu_0 What mu equals under null hypothesis
#'
#' @return a vector with first element as question, second element as correct answer, and other elements as other answer choices.
#' @export
#'
#' @examples makeQA_HypothesisTest(type = 0)
#' "H_0: mu = 4.4; H_a = mu < 4.4. You take 43 samples and find that the sample mean is 4.312. The sample standard deviation is 1.9. Do you reject the null hypothesis at the 0.05 level?"
#' "yes"
#' "no"
#'
#' makeQA_HypothesisTest(type = 1)
#' "H_0: mu = 7; H_a = mu > 7. You take 65 samples and find that the sample mean is 7.109. The sample standard deviation is 4.2. Do you reject the null hypothesis at the 0.05 level?"
#' "no"
#' "yes"
makeQA_HypothesisTest = function(type = NULL, level = 0.05, Xbar = NULL, sigma = NULL, n = NULL, mu_0 = NULL){
if(level >0.5){
stop("Level must be no greater than 0.5")
}
if(is.null(sigma)){
sigma = sample(seq(1, 5, 0.1), 1)
}
if(is.null(n)){
n = sample(30:100, 1)
}
if(is.null(type)){
type = sample(0:2, 1)
}
if(is.null(mu_0)){
mu_0 = round(sample(seq(-10, 10, 0.1),1),2)
}
if(type == 0){ #1 sided, H_a <
if(is.null(Xbar)){
reject = sample(c(0,1), 1)
error = runif(1, -.2, .2)
Xbar = round(mu_0 - (qt(1 - level, n-1) + error + 0.5*reject)*sigma/n, 3)
}
else{
reject = Xbar <= mu_0 - qt(1 - level, n-1)*sigma/n
}
question = paste("$H_0: \\mu = ", mu_0,"$; $H_a: \\mu < ", mu_0,"$. You take ", n," samples and find that the sample mean is ", Xbar,
". The sample standard deviation is ", sigma, ". Do you reject the null hypothesis at the ", level, " level?", sep = "")
yesno = c("no", "yes")
ans1 = yesno[reject + 1]
ans2 = yesno[-(reject + 1)]
answers = c(ans1, ans2)
return(c(question, answers))
}
if(type == 1){ #1 sided, H_a >
if(is.null(Xbar)){
reject = sample(c(0,1), 1)
error = runif(1, -.2, .2)
Xbar = round(mu_0 + (qt(1 - level, n-1) + error + 0.5*reject)*sigma/n, 3)
}
else{
reject = Xbar >= mu_0 - qt(1 - level, n-1)*sigma/n
}
question = paste("$H_0: \\mu = ", mu_0,"$; $H_a: \\mu > ", mu_0,".$ You take ", n," samples and find that the sample mean is ", Xbar,
". The sample standard deviation is ", sigma, ". Do you reject the null hypothesis at the ", level, " level?", sep = "")
yesno = c("no", "yes")
ans1 = yesno[reject + 1]
ans2 = yesno[-(reject + 1)]
answers = c(ans1, ans2)
return(c(question, answers))
}
if(type ==2){ #2 sided
if(is.null(Xbar)){
direction = sample(c(-1,1), 1)
reject = sample(c(0,1), 1)
error = runif(1, -.2, .2)
Xbar = round(mu_0 + direction*(qt(1 - 0.5*level, n-1) + error + 0.5*reject)*sigma/n, 3)
}
else{
reject = Xbar >= mu_0 - qt(1 - 0.5*level, n-1)*sigma/n | Xbar <= mu_0 - qt(1 - 0.5*level, n-1)*sigma/n
}
question = paste("$H_0: \\mu = ", mu_0,"$; $H_a: \\mu \\neq ", mu_0,"$. You take ", n," samples and find that the sample mean is ", Xbar,
". The sample standard deviation is ", sigma, ". Do you reject the null hypothesis at the ", level, " level?", sep = "")
yesno = c("no", "yes")
ans1 = yesno[reject + 1]
ans2 = yesno[-(reject + 1)]
answers = c(ans1, ans2)
return(c(question, answers))
}
}
#' Generate conditional probability question
#'
#' @param proportion Splits the population into 3 groups with this proportion. Must sum to 1
#' @param condprob Gives a conditional probability for each group
#' @param type (1, 2). 1: Total probability question 2: Bayes Theorem question
#'
#' @return a vector with first element as question, second element as correct answer, and other elements as other answer choices.
#' @export
#'
#' @examples makeQA_ConditionalProbability(type = 2)
#' "A company buys resistors from vendor companies A, B, and C.
#' 30% come from company A 40% come from comapny B, and 30% come
#' from company C. If a resistor comes from company A, there is a
#' 67% chance that it is within tolerance. If a resistor comes from
#' company B, there is a 57% chance that it is within tolerance.
#' If a resistor comes from company C, there is a 82% chance that
#' it is within tolerance. If a randomly selected resistor is
#' within tolerance, what is the probability it came from company A?"
#' "0.298"
#' "0.67"
#' "0.675"
#' "0.687"
#' "2.06"
#'
makeQA_ConditionalProbability = function(proportion = NULL, condprob = NULL, type = NULL){
if(is.null(proportion) && is.null(condprob)){
proportion = rep(0, 3)
proportion[1] = sample(seq(0.1, 0.7, 0.1), 1)
proportion[2] = sample(seq(0.1, 1 - proportion[1] - 0.2, 0.1), 1)
proportion[3] = 1 - proportion[1] - proportion[2]
}
if(is.null(proportion)){
n = length(condprob)
proportion = rep(0, n)
proportion[1] = sample(seq(0.1, 0.4, 0.1), 1)
probsum = proportion[1]
for(i in 2:{n-1}){
proportion[i] = sample(seq(0.1, 1 - probsum - 0.1*{3-i}, 0.1), 1)
probsum = probsum + proportion[i]
}
proportion[n] = 1 - probsum
}
if(is.null(condprob)){
condprob = round(runif(length(proportion), 0.2, 0.95), 2)
}
if(sum(condprob > 1) !=0 || sum(condprob < 0) !=0){
stop("Conditional probability outside valid domain.")
}
if(length(proportion) != 3 || length(condprob) != 3){
stop("proportion or conditional probability vector must be null or 3")
}
if(is.null(type)){
type = sample(1:2, 1)
}
if(type == 1){
question = paste("A company buys resistors from vendor companies A, B, and C. ",
100*proportion[1], "\\% come from company A ",
100*proportion[2], "\\% come from company B, and ",
100*proportion[3], "\\% come from company C. If a resistor comes from company A, there is a ",
100*condprob[1], "\\% chance that it is within tolerance. If a resistor comes from company B, there is a ",
100*condprob[2], "\\% chance that it is within tolerance. If a resistor comes from company C, there is a ",
100*condprob[3], "\\% chance that it is within tolerance. If a resistor is randomly sampled, what is the probability it is within tolerance?", sep = "")
ans1 = round(sum(proportion*condprob), 3)
ans2 = round(mean(condprob), 3)
ans3 = round(mean(proportion), 3)
ans4 = sum(condprob)
ans5 = round(mean(proportion)*mean(condprob), 3)
answers = c(ans1, ans2, ans3, ans4, ans5)
return(c(question, answers))
}
if(type == 2){
question = paste("A company buys resistors from vendor companies A, B, and C. ",
100*proportion[1], "\\% come from company A ",
100*proportion[2], "\\% come from comapny B, and ",
100*proportion[3], "\\% come from company C. If a resistor comes from company A, there is a ",
100*condprob[1], "\\% chance that it is within tolerance. If a resistor comes from company B, there is a ",
100*condprob[2], "\\% chance that it is within tolerance. If a resistor comes from company C, there is a ",
100*condprob[3], "\\% chance that it is within tolerance. If a randomly selected resistor is within tolerance, what is the probability it came from company A?", sep = "")
ans1 = round(proportion[1]*condprob[1] / sum(proportion*condprob), 3)
ans2 = condprob[1]
ans3 = sum(proportion*condprob)
ans4 = round(mean(condprob), 3)
ans5 = sum(condprob)
answers = c(ans1, ans2, ans3, ans4, ans5)
return(c(question, answers))
}
}
rearrange = function(x){
num_ques = length(x)
for(i in 1:num_ques){
if(length(x[[i]]) < 2){
stop("All entries of the list must have a question and a correct answer")
}
}
correct = ""
for(i in 1:num_ques){
correct[i] = x[[i]][2]
}
QA = rep(NA, num_ques)
for(i in 1:num_ques){
QA[i] = length(x[[i]]) # number of answers +1 per question
}
ind = sample(num_ques)
reorder_ans = x
for(i in 1:num_ques){
num_ans = length(x[[i]]) #technically number of answers + 1
ind_ans = sample(2:num_ans)
for(j in 2:num_ans){
reorder_ans[[i]][j] = x[[i]][ind_ans[j - 1]]
}
}
reorder_x = list(NA)
reorder_QA = rep(NA, num_ques)
reorder_correct = ""
for(i in 1:num_ques){
reorder_x[i] = reorder_ans[ind[i]]
reorder_QA[i] = QA[ind[i]]
reorder_correct[i] = correct[ind[i]]
}
letter_correct = rep(0, num_ques)
for(i in 1:num_ques){
letter_correct[i] = which(reorder_x[[i]] == reorder_correct[i])
}
letters = c("", "a", "b", "c", "d", "e", "f", "g")
letter_correct_out = ""
for(i in 1:num_ques){
letter_correct_out[i] = letters[letter_correct[i]]
}
#Output string of question and answer
#Output number of elements per question(eg 1 question with 3 answers outputs 4)
return(list(reorder_x, letter_correct_out, reorder_correct, reorder_QA))
}
kristynpantoja/statexams documentation built on June 3, 2019, 5:25 a.m.
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generate_probability_rules = function(special = NULL){
if(special == 2){
tenths = seq(0.1, 0.8, 0.1)
prob_a = sample(tenths, 1)
prob_a_un_b = sample(seq(prob_a, 0.9, 0.1))
prob_b = prob_a_un_b - prob_a
prob_a_int_b = 0
return(c(prob_a, prob_b, prob_a_int_b, prob_a_un_b))
}
tenths = seq(0.2, 0.9, 0.1)
prob_a = sample(tenths, 1)
prob_b = sample(tenths, 1)
if(special == 1){
prob_a_int_b = prob_a * prob_b
}
else{
check = 0
while(check < 1.5){ #makes sure rounding doesn't give a bad value and events are dependent
check = 0
prob_a_int_b = round(runif(1, max(0.01, prob_a + prob_b - 1), min(prob_a, prob_b)), digits = 2)
if(prob_a_int_b != prob_a * prob_b){
check = check + 1
}
if(prob_a_int_b >= max(0.01, prob_a + prob_b - 1) & prob_a_int_b < min(prob_a, prob_b)){
check = check + 1
}
}
}
prob_a_un_b = prob_a + prob_b - prob_a_int_b
return(c(prob_a, prob_b, prob_a_int_b, prob_a_un_b))
}
#' Generate probability question
#'
#' @param type Determines the type of probability question. Valid inputs: 1, 2, 3
#'
#' @return a vector with first element as question, second element as correct answer, and other elements as other answer choices.
#' @export
#'
#' @examples makeQA_EventProbability(type = 1)
#' "Events A and B are independent.The probability of A is 0.9. The probability of B is 0.3. What is the probability that neither A nor B will occur?"
#' "0.070"
#' "0.600"
#' "0.270"
#' "1.200"
#' "0.930"
makeQA_EventProbability = function(type = NULL){
#type = 1 gives independence. 2 gives no assumptions. 3 gives mutually exclusive
if(is.null(type)){
type = sample(1:2,1)
}
if(type == 1){
checkques = 0
type.2 = sample(1:3, 1)
if(type.2 == 1){
while(checkques == 0){
probs = generate_probability_rules(1)
question = paste("Events A and B are independent.The probability of A is ", probs[1],
". The probability of B is ", probs[2], ". What is the probability of A intersection B?", sep = "")
ans1 = round(probs[3],3)
ans2 = round(abs(probs[1] - probs[2]),3)
ans3 = round(probs[4],3)
ans4 = round(probs[1] + probs[2],3)
ans5 = round(1 - probs[4],3)
answers = c(ans1, ans2, ans3, ans4, ans5)
if(length(unique(answers)) == 5){
checkques = 1
}
}
return(c(question, answers))
}
if(type.2 ==2){
while(checkques == 0){
probs = generate_probability_rules(1)
question = paste("Events A and B are independent.The probability of A is ", probs[1],
". The probability of B is ", probs[2], ". What is the probability of at least A or B occurring?", sep = "")
ans1 = round(probs[4],3)
ans2 = round(abs(probs[1] - probs[2]),3)
ans3 = round(probs[3],3)
ans4 = round(probs[1] + probs[2],3)
ans5 = round(1 - probs[4],3)
answers = c(ans1, ans2, ans3, ans4, ans5)
if(length(unique(answers)) == 5){
checkques = 1
}
}
return(c(question, answers))
}
if(type.2 ==3){
while(checkques == 0){
probs = generate_probability_rules(1)
question = paste("Events A and B are independent.The probability of A is ", probs[1],
". The probability of B is ", probs[2], ". What is the probability that neither A nor B will occur?", sep = "")
ans1 = round(1 - probs[4], 3)
ans2 = round(abs(probs[1] - probs[2]), 3)
ans3 = round(probs[3], 3)
ans4 = round(probs[1] + probs[2], 3)
ans5 = round(probs[4], 3)
answers = c(ans1, ans2, ans3, ans4, ans5)
if(length(unique(answers)) == 5){
checkques = 1
}
}
return(c(question, answers))
}
}
if(type == 2){
checkques = 0
while(checkques == 0){
probs = generate_probability_rules(0)
question = paste("The probability of A is ", probs[1],
". The probability of B is ", probs[2],
". The probability of A and B both occurring is ", probs[3],
". What is the probability of A or B occurring?", sep = "")
ans1 = round(probs[4],3)
ans2 = round(abs(probs[1] - probs[2]),3)
ans3 = round(probs[3],3)
ans4 = round(probs[1] + probs[2],3)
ans5 = round(1 - probs[4],3)
answers = c(ans1, ans2, ans3, ans4, ans5)
if(length(unique(answers)) == 5){
checkques = 1
}
}
return(c(question, answers))
}
if(type == 3){
checkques = 0
while(checkques == 0){
probs = generate_probability_rules(2)
question = paste("The probability of A is ", probs[1],
". The probability of B is ", probs[2],
". A and B are mutually exclusive. What is the probability of either A or B occurring?", sep = "")
ans1 = probs[1] + probs[2]
ans2 = abs(probs[1] - probs[2])
ans3 = probs[3]
ans4 = probs[4]
ans5 = 1 - probs[4]
answers = c(ans1, ans2, ans3, ans4, ans5)
if(length(unique(answers)) == 5){
checkques = 1
}
}
return(c(question, answers))
}
}
#' Generate expected value function
#'
#' @param prob Vector of probabilities corresponding to values vector. Must sum to 1 and be non-negative
#' @param values Vector of values that r.v. X takes
#'
#' @return a vector with first element as question, second element as correct answer, and other elements as other answer choices.
#' @export
#'
#' @examples makeQA_ExpectedValue(prob = c(0.4, 0.2, 0.4), values = c(2,4,8))
#' "f(2) = 0.4. f(4) = 0.2. f(8) = 0.4. What is the expected value of X?"
#' "4.8"
#' "14"
#' "15"
#' "84.672"
#' "5"
makeQA_ExpectedValue = function(prob = NULL, values = NULL){
if(is.null(prob) & is.null(values)){
n = sample(3:5, 1)
}
else if(is.null(prob) | is.null(values)){
n1 = length(prob)
n2 = length(values)
n = n1 + n2
}
else{
if(length(prob) != length(values)){
stop("prob and values lengths do not agree")
}
n = length(prob)
}
if(!is.null(prob) & sum(prob) != 1){
stop("prob must sum to 1 or be null")
}
if(!is.null(prob) & (sum(prob < 0) != 0)){
stop("prob must be positive")
}
if(is.null(values)){
values = sample(1:20, n)
values = sort(values)
}
if(is.null(prob)){
checkques = 0
while(checkques == 0){
prob = rep(0, n)
sticks = sample((25:90)/100, n-1 , replace = T)
remainprob = 100
for(i in 1:(n-1)){
prob[i] = floor(remainprob * sticks[i])
remainprob = remainprob - prob[i]
}
prob[n] = remainprob
prob = prob/100
question = ""
for(i in 1:n){
question = paste(question, "f(", values[i], ") = ", prob[i], ". ", sep = "")
}
question = paste(question, "What is the expected value of X?", sep = "")
ans1 = round(sum(values * prob), 3)
ans2 = round(sum(values), 3)
ans3 = round(sum(values + prob), 3)
ans4 = round(prod(values + prob), 3)
ans5 = round(mean(values))
answers = c(ans1, ans2, ans3, ans4, ans5)
if(length(unique(answers)) == 5){
checkques = 1
}
}
return(c(question,answers))
}
else{
question = ""
for(i in 1:n){
question = paste(question, "f(", values[i], ") = ", prob[i], ". ", sep = "")
}
question = paste(question, "What is the expected value of X?", sep = "")
ans1 = round(sum(values * prob), 3) #right
ans2 = round(sum(values), 3) #only summing the values
ans3 = round(sum(values + prob), 3) #adding values and prob
ans4 = round(prod(values + prob), 3) #product of (values + prob)
ans5 = round(mean(values)) #ignores probability and treats like sample mean
answers = c(ans1, ans2, ans3, ans4, ans5)
return(c(question,answers))
}
}
#' Generate hypothesis test question
#'
#' @param type Type of test 0: Left tail, 1: Right tail, 2: Two tailed
#' @param level Level of test. Must be great than 0 and less than 0.5
#' @param Xbar Sample mean
#' @param sigma Sample standard deviation
#' @param n Sample size
#' @param mu_0 What mu equals under null hypothesis
#'
#' @return a vector with first element as question, second element as correct answer, and other elements as other answer choices.
#' @export
#'
#' @examples makeQA_HypothesisTest(type = 0)
#' "H_0: mu = 4.4; H_a = mu < 4.4. You take 43 samples and find that the sample mean is 4.312. The sample standard deviation is 1.9. Do you reject the null hypothesis at the 0.05 level?"
#' "yes"
#' "no"
#'
#' makeQA_HypothesisTest(type = 1)
#' "H_0: mu = 7; H_a = mu > 7. You take 65 samples and find that the sample mean is 7.109. The sample standard deviation is 4.2. Do you reject the null hypothesis at the 0.05 level?"
#' "no"
#' "yes"
makeQA_HypothesisTest = function(type = NULL, level = 0.05, Xbar = NULL, sigma = NULL, n = NULL, mu_0 = NULL){
if(level >0.5){
stop("Level must be no greater than 0.5")
}
if(is.null(sigma)){
sigma = sample(seq(1, 5, 0.1), 1)
}
if(is.null(n)){
n = sample(30:100, 1)
}
if(is.null(type)){
type = sample(0:2, 1)
}
if(is.null(mu_0)){
mu_0 = round(sample(seq(-10, 10, 0.1),1),2)
}
if(type == 0){ #1 sided, H_a <
if(is.null(Xbar)){
reject = sample(c(0,1), 1)
error = runif(1, -.2, .2)
Xbar = round(mu_0 - (qt(1 - level, n-1) + error + 0.5*reject)*sigma/n, 3)
}
else{
reject = Xbar <= mu_0 - qt(1 - level, n-1)*sigma/n
}
question = paste("$H_0: \\mu = ", mu_0,"$; $H_a: \\mu < ", mu_0,"$. You take ", n," samples and find that the sample mean is ", Xbar,
". The sample standard deviation is ", sigma, ". Do you reject the null hypothesis at the ", level, " level?", sep = "")
yesno = c("no", "yes")
ans1 = yesno[reject + 1]
ans2 = yesno[-(reject + 1)]
answers = c(ans1, ans2)
return(c(question, answers))
}
if(type == 1){ #1 sided, H_a >
if(is.null(Xbar)){
reject = sample(c(0,1), 1)
error = runif(1, -.2, .2)
Xbar = round(mu_0 + (qt(1 - level, n-1) + error + 0.5*reject)*sigma/n, 3)
}
else{
reject = Xbar >= mu_0 - qt(1 - level, n-1)*sigma/n
}
question = paste("$H_0: \\mu = ", mu_0,"$; $H_a: \\mu > ", mu_0,".$ You take ", n," samples and find that the sample mean is ", Xbar,
". The sample standard deviation is ", sigma, ". Do you reject the null hypothesis at the ", level, " level?", sep = "")
yesno = c("no", "yes")
ans1 = yesno[reject + 1]
ans2 = yesno[-(reject + 1)]
answers = c(ans1, ans2)
return(c(question, answers))
}
if(type ==2){ #2 sided
if(is.null(Xbar)){
direction = sample(c(-1,1), 1)
reject = sample(c(0,1), 1)
error = runif(1, -.2, .2)
Xbar = round(mu_0 + direction*(qt(1 - 0.5*level, n-1) + error + 0.5*reject)*sigma/n, 3)
}
else{
reject = Xbar >= mu_0 - qt(1 - 0.5*level, n-1)*sigma/n | Xbar <= mu_0 - qt(1 - 0.5*level, n-1)*sigma/n
}
question = paste("$H_0: \\mu = ", mu_0,"$; $H_a: \\mu \\neq ", mu_0,"$. You take ", n," samples and find that the sample mean is ", Xbar,
". The sample standard deviation is ", sigma, ". Do you reject the null hypothesis at the ", level, " level?", sep = "")
yesno = c("no", "yes")
ans1 = yesno[reject + 1]
ans2 = yesno[-(reject + 1)]
answers = c(ans1, ans2)
return(c(question, answers))
}
}
#' Generate conditional probability question
#'
#' @param proportion Splits the population into 3 groups with this proportion. Must sum to 1
#' @param condprob Gives a conditional probability for each group
#' @param type (1, 2). 1: Total probability question 2: Bayes Theorem question
#'
#' @return a vector with first element as question, second element as correct answer, and other elements as other answer choices.
#' @export
#'
#' @examples makeQA_ConditionalProbability(type = 2)
#' "A company buys resistors from vendor companies A, B, and C.
#' 30% come from company A 40% come from comapny B, and 30% come
#' from company C. If a resistor comes from company A, there is a
#' 67% chance that it is within tolerance. If a resistor comes from
#' company B, there is a 57% chance that it is within tolerance.
#' If a resistor comes from company C, there is a 82% chance that
#' it is within tolerance. If a randomly selected resistor is
#' within tolerance, what is the probability it came from company A?"
#' "0.298"
#' "0.67"
#' "0.675"
#' "0.687"
#' "2.06"
#'
makeQA_ConditionalProbability = function(proportion = NULL, condprob = NULL, type = NULL){
if(is.null(proportion) && is.null(condprob)){
proportion = rep(0, 3)
proportion[1] = sample(seq(0.1, 0.7, 0.1), 1)
proportion[2] = sample(seq(0.1, 1 - proportion[1] - 0.2, 0.1), 1)
proportion[3] = 1 - proportion[1] - proportion[2]
}
if(is.null(proportion)){
n = length(condprob)
proportion = rep(0, n)
proportion[1] = sample(seq(0.1, 0.4, 0.1), 1)
probsum = proportion[1]
for(i in 2:{n-1}){
proportion[i] = sample(seq(0.1, 1 - probsum - 0.1*{3-i}, 0.1), 1)
probsum = probsum + proportion[i]
}
proportion[n] = 1 - probsum
}
if(is.null(condprob)){
condprob = round(runif(length(proportion), 0.2, 0.95), 2)
}
if(sum(condprob > 1) !=0 || sum(condprob < 0) !=0){
stop("Conditional probability outside valid domain.")
}
if(length(proportion) != 3 || length(condprob) != 3){
stop("proportion or conditional probability vector must be null or 3")
}
if(is.null(type)){
type = sample(1:2, 1)
}
if(type == 1){
question = paste("A company buys resistors from vendor companies A, B, and C. ",
100*proportion[1], "\\% come from company A ",
100*proportion[2], "\\% come from company B, and ",
100*proportion[3], "\\% come from company C. If a resistor comes from company A, there is a ",
100*condprob[1], "\\% chance that it is within tolerance. If a resistor comes from company B, there is a ",
100*condprob[2], "\\% chance that it is within tolerance. If a resistor comes from company C, there is a ",
100*condprob[3], "\\% chance that it is within tolerance. If a resistor is randomly sampled, what is the probability it is within tolerance?", sep = "")
ans1 = round(sum(proportion*condprob), 3)
ans2 = round(mean(condprob), 3)
ans3 = round(mean(proportion), 3)
ans4 = sum(condprob)
ans5 = round(mean(proportion)*mean(condprob), 3)
answers = c(ans1, ans2, ans3, ans4, ans5)
return(c(question, answers))
}
if(type == 2){
question = paste("A company buys resistors from vendor companies A, B, and C. ",
100*proportion[1], "\\% come from company A ",
100*proportion[2], "\\% come from comapny B, and ",
100*proportion[3], "\\% come from company C. If a resistor comes from company A, there is a ",
100*condprob[1], "\\% chance that it is within tolerance. If a resistor comes from company B, there is a ",
100*condprob[2], "\\% chance that it is within tolerance. If a resistor comes from company C, there is a ",
100*condprob[3], "\\% chance that it is within tolerance. If a randomly selected resistor is within tolerance, what is the probability it came from company A?", sep = "")
ans1 = round(proportion[1]*condprob[1] / sum(proportion*condprob), 3)
ans2 = condprob[1]
ans3 = sum(proportion*condprob)
ans4 = round(mean(condprob), 3)
ans5 = sum(condprob)
answers = c(ans1, ans2, ans3, ans4, ans5)
return(c(question, answers))
}
}
rearrange = function(x){
num_ques = length(x)
for(i in 1:num_ques){
if(length(x[[i]]) < 2){
stop("All entries of the list must have a question and a correct answer")
}
}
correct = ""
for(i in 1:num_ques){
correct[i] = x[[i]][2]
}
QA = rep(NA, num_ques)
for(i in 1:num_ques){
QA[i] = length(x[[i]]) # number of answers +1 per question
}
ind = sample(num_ques)
reorder_ans = x
for(i in 1:num_ques){
num_ans = length(x[[i]]) #technically number of answers + 1
ind_ans = sample(2:num_ans)
for(j in 2:num_ans){
reorder_ans[[i]][j] = x[[i]][ind_ans[j - 1]]
}
}
reorder_x = list(NA)
reorder_QA = rep(NA, num_ques)
reorder_correct = ""
for(i in 1:num_ques){
reorder_x[i] = reorder_ans[ind[i]]
reorder_QA[i] = QA[ind[i]]
reorder_correct[i] = correct[ind[i]]
}
letter_correct = rep(0, num_ques)
for(i in 1:num_ques){
letter_correct[i] = which(reorder_x[[i]] == reorder_correct[i])
}
letters = c("", "a", "b", "c", "d", "e", "f", "g")
letter_correct_out = ""
for(i in 1:num_ques){
letter_correct_out[i] = letters[letter_correct[i]]
}
#Output string of question and answer
#Output number of elements per question(eg 1 question with 3 answers outputs 4)
return(list(reorder_x, letter_correct_out, reorder_correct, reorder_QA))
}
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