Question

Types of Tests. For each of the research studies below, select the statistical test that best answers the question. Do not attempt to answer the research questions.

On average, do people run a mile faster in the morning before breakfast than they do in the evening after supper? Is there a difference in level of happiness measured by the number of times laughed per day among people living in various regions of the US: Northeast, West, Mid-West, or South? A researcher wants to know whether violent crimes are related to the phase of the moon. She records the number of crimes reported on days with different phases of the moon: new moon, first quarter, full moon, or last quarter. She then tests that the percentages at each phase are equal. Do men and women differ significantly in their mean diastolic blood pressure levels? The label on bags of apples says net weight 5 pounds.. An inspector selects a sample of 15 bags of apples and calculates the mean and standard deviation. She then compares the sample statistics to the population mean to see whether there is a significant difference.

Answers

1.	One-sample z-test
2.	One-sample t-test
3.	Independent samples t-test
4.	Dependent/paired t-test
5.	ANOVA F-test
6.	Chi-square goodness of fit
7.	Chi-square test of independence

Answer 1

1. Paired t test.

Here we want the test the averages. Observations are taken on same individual for two times and the averages are compared and hence paired t test.

2. ANOVA F test

Here we want to compare the levels of the happiness for the people in different areas. This is the problem of multiple means comparison and hence ANOVA F test.

3. Chi square test of independence.

Here we want to know whether there is relationship in two attributes i.e. violent crimes and phase of the moon. Here we can get the observations in contingency table and hence chi square test of independence.

4. Independent samples t test.

Here we want to test the means of the blood pressure for men and women. These two samples are independent and also the population variance is unknown to us and hence independent samples t test.

5. One sample t test.

Here test is performed on one sample of the bags. For that the sample mean and sample standard deviation is calculated that means population standard deviation is unkown. Hence one sample t test.