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SAT and ACT Tests Because they enable efficient procedures
Chapter 6, Problem 17BSC(choose chapter or problem)
Problem 17BSC
SAT and ACT Tests Because they enable efficient procedures for evaluating answers, multiple-choice questions are commonly used on standardized tests, such as the SAT or ACT. Such questions typically have five choices, one of which is correct. Assume that you must make random guesses for two such questions. Assume that both questions have correct answers of “a.”
a. After listing the 25 different possible samples, find the proportion of correct answers in each sample, then construct a table that describes the sampling distribution of the sample proportions of correct responses.
b. Find the mean of the sampling distribution of the sample proportion.
c. Is the mean of the sampling distribution (from part (b)) equal to the population proportion of correct responses? Does the mean of the sampling distribution of proportions always equal the population proportion?
Questions & Answers
QUESTION:
Problem 17BSC
SAT and ACT Tests Because they enable efficient procedures for evaluating answers, multiple-choice questions are commonly used on standardized tests, such as the SAT or ACT. Such questions typically have five choices, one of which is correct. Assume that you must make random guesses for two such questions. Assume that both questions have correct answers of “a.”
a. After listing the 25 different possible samples, find the proportion of correct answers in each sample, then construct a table that describes the sampling distribution of the sample proportions of correct responses.
b. Find the mean of the sampling distribution of the sample proportion.
c. Is the mean of the sampling distribution (from part (b)) equal to the population proportion of correct responses? Does the mean of the sampling distribution of proportions always equal the population proportion?
ANSWER:Answer :
Step 1 of 1 :
Given SAT and ACT Tests Because they enable efficient procedures for evaluating answers, multiple-choice questions are commonly used on standardized tests, such as the SAT or ACT. Such questions typically have five choices, one of which is correct.
a).
The possibilities are: both questions incorrect, one question correct (two choices), both questions correct.
The sample proportion is the number of correct answers in the sample divided by the number of answers.
Assign every sample as an equal probability.
Add the probabilities for each sample value.
Then the table is given below.
Sample |
Sample Proportion |
Probability |
aa |
1 |
1/25 |
ab |
0.5 |
1/25 |
ac |
0.5 |
1/25 |
ad |
0.5 |
1/25 |
ae |
0.5 |
1/25 |
ba |
0.5 |
1/25 |
bb |
0 |