Question

The average retirement age in America is 64 years old. Do small business owners retire at a younger average age? The data below shows the results of a survey of small business owners who have recently retired. Assume that the distribution of the population is normal.

69, 53, 50, 58, 69, 68, 68, 51, 70, 67, 60, 55, 63, 56, 53, 69

What can be concluded at the the αα = 0.10 level of significance level of significance?

1. For this study, we should use Select an answer t-test for a population mean z-test for a population proportion
2. The null and alternative hypotheses would be:

H0:H0:  ? p μ  Select an answer ≠ < = >       

H1:H1:  ? p μ  Select an answer > = ≠ <    

3. The test statistic ? t z  =  (please show your answer to 3 decimal places.)
4. The p-value =  (Please show your answer to 4 decimal places.)
5. The p-value is ? ≤ >  αα
6. Based on this, we should Select an answer accept fail to reject reject  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest the population mean retirement age for small business owners is not significantly younger than 64 at αα = 0.10, so there is insufficient evidence to conclude that the population mean retirement age for small business owners is younger than 64.
   • The data suggest the populaton mean is significantly younger than 64 at αα = 0.10, so there is sufficient evidence to conclude that the population mean retirement age for small business owners is younger than 64.
   • The data suggest the population mean is not significantly younger than 64 at αα = 0.10, so there is sufficient evidence to conclude that the population mean retirement age for small business owners is equal to 64.

Answer 1

From the givend data

a) t-test for a population mean is used for this data

since Population SD is not known

b) H0: The population mean retirement age for small business owners is not younger than 64.

H1: The population mean retirement age for small business owners is younger than 64.

i.e. H0:   μ   = 64

H1: μ   < 64

c) Test Statistic;

d) P-value = 0.0758

e) P-value < alpha 0.10

f) since P-value < alpha 0.10 so we reject H0

g) Correct answer:

The data suggest the populaton mean is significantly younger than 64 at αα = 0.10, so there is sufficient evidence to conclude that the population mean retirement age for small business owners is younger than 64.