Deck 7: The Single-Sample Z Test

Question 1

A researcher is interested in whether students who are musicians have higher intelligence test scores than students in the general population. The researcher predicts that playing a musical instrument is associated with higher intelligence test scores. The researcher selects a sample of 75 musicians from local high schools and gives them an intelligence test. She compares their average intelligence to that of students in the general population and finds that z_obt = +1.92. This is a _____ test and the researcher should conclude _____.

A) one-tailed; that students who are musicians score significantly higher on intelligence tests
B) two-tailed; that students who are musicians score significantly higher on intelligence tests
C) one-tailed; that students who are musicians do not score significantly higher on intelligence
Tests
D) two-tailed; that students who are musicians do not score significantly higher on intelligence
Tests

Answer 1

one-tailed; that students who are musicians score significantly higher on intelligence tests

Question 2

Which of the following might one do in order to increase the power of a z test?

A) Increase the sample size.
B) Use a two-tailed test.
C) Decrease sample size.
D) None of the above.

Answer 2

Increase the sample size.

Question 3

Given: For one section of the SAT: $\mu$ = 500 and $\sigma$ = 100. The SAT was given to a sample of N = 35 and the mean SAT for this sample was 536. Calculate the z test for this sample mean. Does this sample differ significantly from the population for a two-tailed test?

Answer 3

The z test score is 2.13. Thus, with z_cv = 1.96, this sample mean differs significantly from the population mean.

Question 4

A researcher is interested in whether students who attend private elementary schools do better or worse on a standard test of intelligence than the general population of elementary school children. A random sample of 75 students at a private elementary school is tested and has a mean intelligence test score of 103.5. The average for the general population of elementary school children is 100 ( $\sigma$ = 15).

-Is this a one- or two-tailed test?

Question 5

A researcher is interested in whether students who attend private elementary schools do better or worse on a standard test of intelligence than the general population of elementary school children. A random sample of 75 students at a private elementary school is tested and has a mean intelligence test score of 103.5. The average for the general population of elementary school children is 100 ( $\sigma$ = 15).

-What are H0 and Ha for this study?

Question 6

A researcher is interested in whether students who attend private elementary schools do better or worse on a standard test of intelligence than the general population of elementary school children. A random sample of 75 students at a private elementary school is tested and has a mean intelligence test score of 103.5. The average for the general population of elementary school children is 100 ( $\sigma$ = 15).

-Compute Z_obt.

Question 7

A researcher is interested in whether students who attend private elementary schools do better or worse on a standard test of intelligence than the general population of elementary school children. A random sample of 75 students at a private elementary school is tested and has a mean intelligence test score of 103.5. The average for the general population of elementary school children is 100 ( $\sigma$ = 15).

-What is z_cv?

Question 8

A researcher is interested in whether students who attend private elementary schools do better or worse on a standard test of intelligence than the general population of elementary school children. A random sample of 75 students at a private elementary school is tested and has a mean intelligence test score of 103.5. The average for the general population of elementary school children is 100 ( $\sigma$ = 15).

-Should H₀ be rejected? What should the researcher conclude?

Question 9

A researcher is interested in whether students who attend private elementary schools do better or worse on a standard test of intelligence than the general population of elementary school children. A random sample of 75 students at a private elementary school is tested and has a mean intelligence test score of 103.5. The average for the general population of elementary school children is 100 ( $\sigma$ = 15).

-Calculate the 95% confidence interval for the population mean based on the sample mean.

Question 10

Explain why decreases as the size of the samples in the sampling distribution increases. Your answer should include an explanation based on the formula for and an explanation of why this formula makes sense (in other words, why would increasing the size of each sample in the sampling distribution cause to decrease?).