It is known that the population mean for the Quantitative section of the GRE is 500, with a

Question

It is known that the population mean for the Quantitative section of the GRE is 500, with a

standard deviation of 100. In 2006, a sample of 400 students taking the GRE, whose family
income was between $70,000 and $80,000, had a quantitative GRE score of 511. Perform a
one-tailed hypothesis test to determine whether the group, whose family income was between
$70,000 and $80,000, scored significantly higher on average than the population.
8. What is the appropriate hypothesis test?
a. z-test
b. t-test for matched pairs
c. t-test for independent samples
d. chi square test for independence
9. What are the null and alternative hypotheses?
a. H0:μ=μ0; Ha:μ<μ0
b. H0:μ=μ0; Ha:μ>μ0
c. H0:μ=μ0; Ha:μ≠μ0
d. None of these are correct

Answer 1

To determine the appropriate hypothesis test, we need to consider the nature of the data and the objectives of the study. In this case, we are comparing the sample mean (quantitative GRE score for students with a family income between $70,000 and $80,000) to a known population mean.

Since we have a known population standard deviation and are comparing the sample mean to a known population mean, the appropriate hypothesis test is a z-test (option a).

For the null and alternative hypotheses, we need to state the hypotheses based on the research question and the direction of the comparison.

The null hypothesis (H0) states that there is no significant difference between the average quantitative GRE score for students with a family income between $70,000 and $80,000 and the population mean. In this case, the null hypothesis is that the population mean (μ) is equal to the known population mean (μ0).

The alternative hypothesis (Ha) states that there is a significant difference, specifically that the average quantitative GRE score for students with a family income between $70,000 and $80,000 is higher than the population mean. In this case, the alternative hypothesis is that the population mean (μ) is greater than the known population mean (μ0).

Therefore, the correct answer for question 9 is b. H0:μ=μ0; Ha:μ>μ0.

It is known that the population mean for the Quantitative section of the GRE is 500, with a

8. A

To determine the appropriate hypothesis test, we need to consider the nature of the data and the objectives of the study. In this case, we are comparing the sample mean (quantitative GRE score for students with a family income between $70,000 and $80,000) to a known population mean.