Question

The U.S. Bureau of Labor and

Statistics reported that a person between the ages of
18 and 34 has had an average of 9.2 jobs. To see if this
average is correct, a researcher selected a sample of 8
workers between the ages of 18 and 34 and asked how
many different places they had worked. The results
were as follows:
8 12 15 6 1 9 13 2
At 0.05 can it be concluded that the mean is 9.2?
Give one reason why the respondents might not have given
the exact number of jobs that they have worked.

Answer 1

The solution to the problem is shown below:Step 1: We have n=8, and the null hypothesis isHo: µ=9.2against the alternative hypothesisHa: µ≠9.2Step 2: At 0.05, the rejection region is two-tailed and equals 2.306.Step 3: The mean of the data is given bySumming all the data together, we get: 8+12+15+6+1+9+13+2=66Therefore, the sample mean is given byThe sample mean is 8.25.Step 4: The sample variance is given byTherefore, the sample variance is 25.89.Step 5: The standard deviation of the sample is the square root of the variance orTherefore, the standard deviation of the sample is 5.09.Step 6: We find the t-score byTherefore, the t-score is -1.022.Step 7: Since t-score (-1.022) is less than the critical value 2.306, we fail to reject the null hypothesis. Hence, there is insufficient evidence to support the claim that the mean number of jobs for people aged 18 to 34 is 9.2. So, we cannot conclude that the mean is 9.2.Give one reason why the respondents might not have given the exact number of jobs that they have worked.The following are the reasons why respondents might not have given the exact number of jobs they have worked:There may be confidentiality issues involved in disclosing previous employers.There may be negative feelings towards former employers, which could influence the responses of the respondents.There may be a variation in the number of jobs worked because some people work multiple part-time jobs while others work a single full-time job, affecting the number of jobs held over time.