The government's claims that students earn an average of $4,500 during their summer break from studies. A random sample of students gave had a sample average of $3,975 and a 95% confidence interval was found to be $3,525 < µ < $4,425. This interval is interpreted to mean that:

a. because our specific confidence interval does not contain the value $4500 there is a 95% probability that the true average summer earnings is not $4500. b. if we were to repeat our survey many times, then about 95% of all the confidence intervals will contain the value $4500. c. if we repeat our survey many times, then about 95% of our confidence intervals will contain the true value of the average earnings of students. d. there is a 95% probability that the true average earnings are between $3525 and $4425 for all students.

Question

Christina

Mathematics

1 November, 21:09

The government's claims that students earn an average of $4,500 during their summer break from studies. A random sample of students gave had a sample average of $3,975 and a 95% confidence interval was found to be $3,525 < µ < $4,425. This interval is interpreted to mean that:

a. because our specific confidence interval does not contain the value $4500 there is a 95% probability that the true average summer earnings is not $4500. b. if we were to repeat our survey many times, then about 95% of all the confidence intervals will contain the value $4500. c. if we repeat our survey many times, then about 95% of our confidence intervals will contain the true value of the average earnings of students. d. there is a 95% probability that the true average earnings are between $3525 and $4425 for all students.

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Answers (1)

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Marisol Flynn · Answer 1

d. there is a 95% probability that the true average earnings are between $3525 and $4425 for all students.

Step-by-step explanation:

95% confidence interval $3,525 < µ < $4,425 suggests that (choice d) there is a 95% probability that the true average earnings are between $3525 and $4425 for all students.

This result also suggests that (choice a) the true average summer earnings is not $4500, because our specific confidence interval does not contain the value $4500. But 95% probability is about the interval $3,525 < µ < $4,425, not the value $4500.