# an explanation of the difference between one sample and two sample hypothesis testing

Problem 1

Write a brief explanation of the difference between one sample and two sample hypothesis testing?

Problem 2: T-test of means (one variable: testing sample measure as proxy for population)

Use the GSSFT (General Social Security Full Time) data set to complete the following problem.

Test the hypothesis that for all full-time workers, the population value for average hours worked is 40 hours (variable hrs1).  You will use the one-sample t-test.

b)  What is the null hypothesis that you want to test? The alternative hypothesis?

c)   Test the hypothesis and write a brief summary of your conclusions.

d)   Based on the 95% confidence interval for the mean difference, can you reject the null hypothesis that the average population value for hours is 43 hours? Explain.

Problem 3:  T-test means (two variables: testing sample measures as proxy for population in comparison to one another)

Use the Country data set to complete the following problem. Test the hypothesis that the average life expectancy for males is the same as the average life expectancy for females (variables: lifeexpm and lifeexpf). Use the paired samples t-test.

a)  What is the null hypothesis? What is the alternative hypothesis?

b)  Look at the distribution of the differences. Summarize your conclusions and state whether there is a statistical difference in life expectancies.

Problem 4

Use the 04cars dataset. Compute a new variable called markup = ((suggretail-dealercost)/dealercost)*100. You will use the “Transform>Compute Variable” dialog. You will test the hypothesis that Sports Cars have a higher markup than other cars.

a) Formulate the null hypothesis that you want to test? The alternative hypothesis?

b) Which type of t-test will be used to evaluate your hypothesis? What are you choosing this method?

c) Test the hypothesis and write a brief summary of your conclusions.

Problem 5

Use the School Salary data set.  You are asked to investigate if male and female school superintendents earn the same pay? Salaries for 20 males and 17 females in a certain metropolitan area are given in the school salary dataset. At α = .01, were the mean superintendent salaries greater for men than for women? Note that the gender variable is called male and is coded 0,1 (0 indicating female and 1 indicating male, using the coding protocol 0 is not and 1 is.)

(a) State both hypotheses (Ho and Ha).

(b) State the decision rule and sketch it as a bell curve diagram.

(c) Conduct an independent T-test of the above hypothesis and state your findings.

After completing the problems:

1.  Copy the relevant SPSS output to a MS Word document. (You can simply copy and paste or you can export the file while in SPSS.)