Question

8. Last year, the U.S. mean hourly rate was $12.45. In April of this year, a sample of 50 workers showed an average hourly rate of $13.76 with a standard deviation of $3.01. Use a=05. Would you conclude hourly rates this year are higher than last year rates?

A: no, because p-value (.0017) is less than a=.05 (I used t)

B: no, because p-value (.0010) is less than a=.05 (I used z)

C: yes, because p-value (.0017) is less than a=.05 (I used t)

D: yes, because p-value (.0010) is less than a=.05 (I used z)

Answer 1

To test against

Here

sample mean

sample standard deviation

and sample size

The test statistic can be written as

which under H₀ follows a t distribution with n-1 df.

We reject H₀ at 0.05 level of significance if P-value < 0.05

Now,

The value of the test statistic

P-value =

Conclusion : C: yes, because p-value (.0017) is less than a=.05 (I used t)

Now,

The value of the test statistic =