In: Statistics and Probability
The average retirement age in America is 64 years old. Do small business owners retire at a different 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.
57, 65, 50, 57, 65, 63, 63, 59, 54, 66, 53, 51, 68
What can be concluded at the αα = 0.01 level of significance?
H0:
H1:
Solution:
First need to find mean and standard deviation from given data,
Therefore, mean and standard deviation is,
For this study, we should use: This corresponds to a two-tail test, for which a t-test for one mean, with unknown population standard deviation will be used.
The null and alternative hypotheses would be:
The number of degrees of freedom are df = n-1 = 13-1=12
Rejection Region:
Given significance level = α = 0.01 and df = 12
The p-value = 0.0169 (Please show your answer to 4 decimal places.)
The p-value is greater than α
Based on this, we should: fail to reject the null hypothesis.
Thus, the final conclusion is that The data suggest the population mean retirement age for small business owners is not significantly different from 64 at α = 0.01, so there is insufficient evidence to conclude that the population mean retirement age for small business owners is different from 64.