Question

Testing a claim about a mean with unknown σ

The mean age of cars driven by commuting college students is 7 years. The Dean claims that this is an accurate statement for his students. A random sample of 31 cars in the East Student parking Lot on campus showed a mean age of 8.1 years with a standard deviation of 5.1 years. Test the Dean’s claim at the α= .05 level of significance.

1.Are the necessary conditions met?

2. Simple random sample?

3. Sample size > 30?                                 (If yes, we don’t have to worry about the distribution)

Since σ is unknown, we will use the t distribution.

4. Write the claim in words:

5. Translate the claim into symbols:

6. Create the null and alternative hypotheses:

7. Identify the type of test (left-tailed, right-tailed, two-tailed):

8. Compute the test statistic   t=x-μxsn                            s=                n=          

9. Substitute and simplify    t=

10. Critical Value Method: Compare the test statistic with the critical value to make a decision about rejecting .

11. Find the critical t values.   The df =       , identifying the row in the t table.

-Two-tailed test, so go to the “area in two tails 0.05” column.

12. Read t = ± , since it is a two-tailed test in a symmetric distribution.

13. Draw a student t distribution. Shade the critical regions and locate the test statistic on the horizontal axis. Is the test statistic in the critical region?

14. Form a conclusion:

15. P-value method: Compare the P-value with the level of significance to make a decision about rejecting . You would need to examine the values in the df row to find a range of values for the P-value – not practical without technology.

16. If P-value ≤ α, we reject the null hypothesis. If P-value > α, we fail to reject the null hypothesis.

Answer 1

------------------------------------------------------------------------------------------------------------------------------