Question

Suppose that a recent issue of a magazine reported that the average weekly earnings for workers who have not received a high school diploma is $495. Suppose you would like to determine if the average weekly for workers who have received a high school diploma is significantly greater than average weekly earnings for workers who have not received a high school diploma. Data providing the weekly pay for a sample of 50 workers are available in the file named WeeklyHSGradPay. These data are consistent with the findings reported in the article.

Weekly Pay

687.73	543.15	789.45	442.26	684.85	661.43	478.3	629.62	486.95	786.47
652.15	652.82	669.81	641.13	577.24	845.68	541.59	553.36	743.25	468.61
821.71	757.82	657.34	506.95	744.93	553.2	827.92	663.85	685.9	637.25
530.54	515.85	588.77	506.62	720.84	503.01	583.18	7,980.24	465.55	593.12
605.33	701.56	491.86	763.4	711.19	631.73	605.89	828.37	477.81	703.06

(a)

State the hypotheses that should be used to test whether the mean weekly pay for workers who have received a high school diploma is significantly greater than the mean weekly pay for workers who have not received a high school diploma. (Enter != for ≠ as needed.)

H₀:

$$μ≤495

  

H_a:

$$μ>495

  

(b)

Use the data in the file named WeeklyHSGradPay to compute the sample mean, the test statistic, and the p-value. (Round your sample mean to two decimal places, your test statistic to three decimal places, and your p-value to four decimal places.)

sample mean= test statistic=18.542 p-value=

(c)

Use

α = 0.05.

What is your conclusion?

Reject H₀. We can not conclude that the mean weekly pay for workers who have received a high school diploma is higher than that for workers who have not received a high school diploma.Reject H₀. We can conclude that the mean weekly pay for workers who have received a high school diploma is higher than that for workers who have not received a high school diploma.    Do not reject H₀. We can not conclude that the mean weekly pay for workers who have received a high school diploma is higher than that for workers who have not received a high school diploma.Do not reject H₀. We can conclude that the mean weekly pay for workers who have received a high school diploma is higher than that for workers who have not received a high school diploma.

(d)

Repeat the hypothesis test using the critical value approach.

State the null and alternative hypotheses. (Enter != for ≠ as needed.)

H₀:

$$μ≤495

  

H_a:

$$μ>495

  

Find the value of the test statistic. (Round your answer to three decimal places.)

18.542

State the critical values for the rejection rule. (Round your answers to three decimal places. If the test is one-tailed, enter NONE for the unused tail.)

test statistic≤NONE test statistic≥

State your conclusion.

Reject H₀. We can not conclude that the mean weekly pay for workers who have received a high school diploma is higher than that for workers who have not received a high school diploma.Reject H₀. We can conclude that the mean weekly pay for workers who have received a high school diploma is higher than that for workers who have not received a high school diploma.    Do not reject H₀. We can not conclude that the mean weekly pay for workers who have received a high school diploma is higher than that for workers who have not received a high school diploma.Do not reject H₀. We can conclude that the mean weekly pay for workers who have received a high school diploma is higher than that for workers who have not received a high school diploma.

Answer 1

a)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ <= 495
Alternative Hypothesis, Ha: μ > 495

b)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (778.01 - 495)/(1045.1322/sqrt(50))
t = 1.915

P-value Approach
P-value = 0.0307

c)

Reject H0. We can conclude that the mean weekly pay for workers who have received a high school diploma is higher than that for workers who have not received a high school diploma.

d)
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ <= 495
Alternative Hypothesis, Ha: μ > 495

Rejection Region
This is right tailed test, for α = 0.05 and df = 49
Critical value of t is 1.677.
Hence reject H0 if t > 1.677

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (778.01 - 495)/(1045.1322/sqrt(50))
t = 1.915

Reject H0. We can conclude that the mean weekly pay for workers who have received a high school diploma is higher than that for workers who have not received a high school diploma.