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.

64, 59, 67, 58, 54, 63, 54, 63, 62, 56, 59, 67

What can be concluded at the the αα = 0.01 level of significance level of significance?

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

H0:H0:  ? μ p  ? ≠ > < =       

H1:H1:  ? μ p  ? = > ≠ <    

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 fail to reject reject accept  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest the populaton mean is significantly younger than 64 at αα = 0.01, 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 = 0.01, so there is sufficient evidence to conclude that the population mean retirement age for small business owners is equal to 64.
   • The data suggest the population mean retirement age for small business owners is not significantly younger than 64 at αα = 0.01, so there is insufficient evidence to conclude that the population mean retirement age for small business owners is younger than 64.

Answer 1

a) For this study, we should use Select an t-test for a population mean.

b) Null and alternative hypothesis is

H0 : u = 64

H1 : u >  64

c)

n =12

sample mean =

standard deviation = S = 4.5427

Level of significance = 0.01

Here population standard deviation is not known so we use t-test statistic.

Test statistic is

d)

Degrees of freedom = n - 1 = 12 - 1 = 11

P-value =0.0109 ( using t table)

P-value , Failed to Reject H0

f) Based on this, we should Select an answer fail to reject the null hypothesis.

g) conclusion : The data suggest the population mean is not significantly younger than 64 at

α = 0.01, so there is sufficient evidence to conclude that the population mean retirement age for small business owners is equal to 64.