Question

8. An employment information service claims the mean annual pay for​ full-time male workers over age 25 without a high school diploma is ​$22 comma 325. The annual pay for a random sample of 10 ​full-time male workers over age 25 without a high school diploma is listed. At alphaequals0.01​, test the claim that the mean salary is ​$22 comma 325. Assume the population is normally distributed. 20 comma 654 21 comma 139 22 comma 352 21 comma 391 22 comma 977 16 comma 910 19 comma 160 23 comma 199 24 comma 187 26 comma 283 ​(a) Write the claim mathematically and identify Upper H 0 and Upper H Subscript

a. Which of the following correctly states Upper H 0 and Upper H Subscript a​? A. Upper H 0​: muequals22 comma 325 Upper H Subscript a​: muless than22 comma 325 B. Upper H 0​: munot equals22 comma 325 Upper H Subscript a​: muequals22 comma 325 C. Upper H 0​: muequals22 comma 325 Upper H Subscript a​: mugreater than22 comma 325 D. Upper H 0​: mugreater than or equals22 comma 325 Upper H Subscript a​: muless than22 comma 325 E. Upper H 0​: muequals22 comma 325 Upper H Subscript a​: munot equals22 comma 325 F. Upper H 0​: mugreater than22 comma 325 Upper H Subscript a​: muless than or equals22 comma 325 ​

(b) Find the critical​ value(s) and identify the rejection​ region(s). What​ is(are) the critical​ value(s), t 0​? t 0equals nothing ​(Use a comma to separate answers as needed. Round to three decimal places as​ needed.)

Which of the following graphs best depicts the rejection region for this​ problem? A. 0 nbsp t 0 A normal curve is over a horizontal axis and is centered at 0. Vertical line segments extend from the horizontal axis to the curve at t@Sub{0}, where t@Sub{0} is to the left of 0. The area under the curve to the left of t@Sub{0} is shaded. B. 0 nbsp t 0 A normal curve is over a horizontal axis and is centered at 0. Vertical line segments extend from the horizontal axis to the curve at t@Sub{0}, where t@Sub{0} is to the right of 0. The area under the curve to the right of t@Sub{0} is shaded. C. 0 nbsp t 0negative t 0 A normal curve is over a horizontal axis and is centered at 0. Vertical line segments extend from the horizontal axis to the curve at negative t@Sub{0}, 0 and t@Sub{0}, where negative t@Sub{0} is to the left of 0 and t@Sub{0} is to the right of 0. The area under the curve to the left of negative t@Sub{0} and to the right of t@Sub{0} is shaded.

​(c) Find the standardized test statistic. tequals nothing ​(Round to two decimal places as​ needed.) ​

(d) Decide whether to reject or fail to reject the null hypothesis. A. Reject Upper H 0 because the test statistic is in the rejection region. B. Reject Upper H 0 because the test statistic is not in the rejection region. C. Fail to reject Upper H 0 because the test statistic is in the rejection region. D. Fail to reject Upper H 0 because the test statistic is not in the rejection region. ​(e) Interpret the decision in the context of the original claim. A. There is sufficient evidence to reject the claim that the mean salary is $ 22 comma 325. B. There is not sufficient evidence to reject the claim that the mean salary is not $ 22 comma 325. C. There is sufficient evidence to reject the claim that the mean salary is not $ 22 comma 325. D. There is not sufficient evidence to reject the claim that the mean salary is $ 22 comma 325. Click to select your answer(s).

Answer 1

Given population mean, = 22325

Given no of people in random sample, n = 10

And data set is,

Pay
20654
21139
22352
21391
22977
16910
19160
23199
24187
26283

Given, = 0.01

1.)

So, Null Hypotheses and Alternate Hypotheses is given as:

H_o: = 22325

H_a: 22325

Hence Option E is correct

2.)

For us, n = 10

so, degree of freedom, df = 10 -1 = 9

df = 9

critical values of t for 2 tailed test are:

t_c = -3.25 and

t_c​=3.25

Graphically,

3.)

Test statistic is given as:

Where M = sample mean = sum of 10 observations / 10 = 21825.2

On putting the values in above formula,

t = -0.601

Corresponding p-value is = 0.56

4.)

Since P is not less than 0.01, so results are not significant at alpha = 0.01.

We cannot reject the NUll Hypotheses.

The mean of data set is not significantly different from = 22325.

H_o is accepted

Option D is correct.