**Project: Inference for One Population **

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

__Part
1: Inference on One Population Mean__

The data in http://www.cc.ysu.edu/~ghchang/stat/GSS_20.sav**
**(**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.)

web address for data above:

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, H_{0}: _________________________________

Alternative
hypothesis, H* _{a}*:
_________________________________

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, H_{0}: _________________________________

Alternative
hypothesis, H* _{a}*:
_________________________________

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:

_____________ ± ___________