Project:  Inference for One Population

Course code:  _ _ _ _    Name(s): ________________________, _________________________

Part 1: Inference on One Population Mean

The data in (click and download this file) is a random sample taken from a population. The objective of this project is to determine whether the average age of the sampled population is greater than 40 or not. (Use a at 5% for all test.)

Variable to be studied: age

Consider this is a hypothesis-testing problem and answer the following questions:

1)      State the two statistical hypotheses.

Null hypothesis,                  H0:  _________________________________

Alternative hypothesis,        Ha:  _________________________________

2)      Check the normality condition with SPSS.

What is the p-value from the normality test? ____________

Would you accept the normality assumption? ____________

3)      Use SPSS to find the sample mean and the sample standard deviation.

Sample mean =  __________

Sample standard deviation =  _____________

4)      What is the value of the t-test statistic = _________________

What is the degrees of freedom for this test = __________

What is the p-value for this test? ________________

If the critical value approach is used what is/are the critical value(s)?

__________________

5)      Your conclusion for this test:

6)      Report the 90% confidence interval estimate for the mean age of the population:

_____________   ±  ___________

Part 2: Inference for Proportion

The data is in http://www.cc.ysu.edu/~ghchang/stat/GSS_all.sav (click and download this file,) is a random sample taken from a population. The objective of this project is to determine whether percentage of people voted in 1992 is higher than 70% or not. (Use a at 5% for all test.)

Variable to be studied: vote92

Consider this is a hypothesis-testing problem and answer the following questions:

1)      State the two statistical hypotheses.

Null hypothesis,                  H0:  _________________________________

Alternative hypothesis,        Ha:  _________________________________

2)      What assumption needs to be checked in order to use a z-test and is the large sample assumption valid?

3)      Use the t-test is SPSS to approximate the z-test for proportion.

What is the value of the t-test statistic from SPSS = _________________

What is the calculated z-test statistic value = _________________ (Do this by hand.)

Are t-test statistic and z-test statistic about the same?

What is the 2-tailed p-value reported in SPSS? ______________

What is the p-value for this test? ________________

4)      Your conclusion for this test:

5)      Report the 95% confidence interval estimate for the percentage of the population who voted in 1992:

_____________   ±  ___________