Question

SuperTemps Agency finds it difficult to retain their employees because most of them are looking for full-time positions and will leave the SuperTemps Agency when a good opportunity comes along. For the 32 most recent SuperTemps employees who terminated, the average time of employment was 7.2 months and the standard deviation was 10.5 months. Treat this as a random sample of 32 SuperTemps employees.

Historically, the average length of employment has held steady at 5.0 months. Based on this recent sample of 32 employees, is there sufficient evidence to conclude that the true population average length of employment for SuperTemps Agency employees has increased? Why or why not?

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u < 5.0
Alternative hypothesis: u > 5.0

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 1.85616
DF = n - 1

D.F = 31
t = (x - u) / SE

t = 1.19

where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.

The observed sample mean produced a t statistic test statistic of 1.19.

Thus the P-value in this analysis is 0.122.

Interpret results. Since the P-value (0.122) is greater than the significance level (0.05), we cannot reject the null hypothesis.

From the above test there is not sufficient evidence to conclude that the true population average length of employment for SuperTemps Agency employees has increased.