A student research project suggests that the distance a person lives from home a

Question

A student research project suggests that the distance a person lives from home and college satisfaction are inversely related. Thirty-two participants were enrolled in the study. The distances from home is measured in miles (cannot have 0) and the satisfaction is measured on a 1-10 scale.

Please be sure to answer all the questions #1-#10. Most people do not answer it all the way *************

1.What are the researcher’s independent and dependent variables?

a.Independent=______________________________

b.Dependent=_______________________________

2. What are the null and alternative hypotheses (use the appropriate symbols not words)?

a.H0=__________________

b.H1=__________________

3.What is the appropriate test for the researcher to use?__________________

4.Why is that statistic appropriate?

If applicable to the specific test:

5.What are the test’s assumptions?

6.What are the test’s df?

7.What is the appropriate critical value?

8.If the research obtains a test statistic of .672, would the researcher retain or reject H0?

9.Should the researcher do any follow up tests or make any graphs/charts?

10.Interpret the findings in APA style

Explanation / Answer

Part-1

Independent= Distance a person lives from home

Dependent= College Satisfaction

Part-2

Let College Satisfaction= 0+ 1 Distance

As student research project suggests that the distance a person lives from home and college satisfaction are inversely related, so

H0: 1=0

H1: 1<0

Part-3

Appropriate test is the t-test of significance of slope.

Part-4

This is the sampling distribution of the estimated slope so Student’s t-statistic is appropriate

Part-5

Test assumptions are that errors/residuals are independently and identically distributed as normal distribution with zero mean and constant variance.

Part-6

Degree of freedom=n-2 , where n is sample size

Part-7

Left tailed Critical value is t0.05(n-2)

Part-8

As test statistic is positive and alternative hypothesis is left tailed, so p-value=P(t<0.672) is surely greater than 0.05 and so we do not reject the null hypothesis

Part-9

Yes, residual plot of residual versus fitted value, normal Q-Q plot of residuals and histograms are useful to identify assumptions

Part-10

To know whether the distance a person lives from home and college satisfaction are inversely related, simple linear regression analysis was applied and it was found that the slope is not significant, t(n-2)=0.67, p>0.05. Hence, from the data results it was found that distance a person lives from home and college satisfaction are not inversely related and heave no significant relationship.

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