Good day tutor, could you kindly assist in answering the questions(4-6 only)below.

I have completed 1-3, please also take note of the instruction and data set show below for reference. Thank you

The data set has salaries of recent graduates (within the last five years) from public universities or private universities; (#s 1-6) is about the difference in population means (1 2 )

For Problems1 - 6: A researcher claims that, on average, recent graduates from private universities earn at least $5000 more per year than graduates from public universities. Using the first data set and = 0.01, test if there is evidence against the researcher's claim. That is, test that the difference is not more than $5000

1. Define the parameter(s) in the context of the problem.

Ans: The parameter in this context is the difference in population means between the salaries of recent graduates from private universities and public universities.

2. State the hypotheses for this test.

Ans: The null hypothesis is that the true population mean difference in salaries between recent graduates from private universities and public universities is less than or equal to $5,000.

The alternative hypothesis is that the true population mean difference in salaries between recent graduates from private universities and public universities is greater than $5,000.

3. In the Variable 1 Range field:

Select the Private data - including the "Private University" label In the Variable 2 Range field: select the Public data - including the "Public University" label Enter the hypothesized value for the difference in means (from #2);

Could you also Check the "Labels" box; Enter alpha of 0.01; Select "Output Range" and enter E2 in the field; resize the output for easier reading: double click on the small vertical bars dividers between the column headers of E and F; F and G; and G and H, Finally provide the copy and paste the output from E2:G14

Answer:

Variable 1 Range: Private data - including the "Private University" label.

Variable 2 Range: Public data - including the "Public University" label.

Hypothesized value for the difference in means: 5000

Output from E2:G14:

The p-value is 0.039, which is less than the significance level of 0.01. Therefore, we reject the null hypothesis and conclude that there is sufficient evidence to support the researcher's claim that, on average, recent graduates from private universities earn at least $5000 more per year than graduates from public universities.

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4. Type the probability statement for the p-value and the probability. Round the test statistic to 2 decimals and the p-value to 6 decimals. Showing two p-values (probabilities): one-tailed and two-tailed, select the one that is for the hypothesis from #2.

5. Type the critical value(s) for the rejection region for this test to 6 decimals. Shows the positive critical values for one-tailed and two-tailed tests. The appropriate value(s) is based on the hypothesis from #2

6. Compare the p-value to , or the test statistic to the critical value(s);by typing the conclusion -------------------------------------------------- End -----------------------------------------------------

Please refer to the data set shown below:

Private University	Public University
58878.66	42545.94
72080.56	86914.89
63743.64	93220.61
81018.57	48826.9
77160.13	43750.09
77535.37	56173.95
67803.82	66816.77
102140.13	46175.76
46626.62	86749.49
84375.51	66292.88
46353.33	63892.95
78113.87	51010
58707.28	86749.44
50379.62	45064.9
78358.12	94074.1
97967.97	65357.33
89501.6	73412.55
51540.79	50695.4
71850.34	58633.43
40894.52	53232.85
70022	95903.43
93974.41	81920.95
77537.06	73597.29
83668.64	81524.29
91611.48	54405.88
80122.97	52392.3
81539.11	67387.46
65772.14	87761.65
46064.45	54507.48
73574.09	92895.5
80431.85	88532.74
56644.22	41897.89
57871.52	43762.43
69004.35	65984.03
65509.34	87000.55
48623.15	75807.69
43628.01	66740.78
91006.87	82703.64
56022.63	58424.15
66304.41	65462.2
61790.77	39982.5
75857.16	84752.09
60951.87	52028.49
64730.12	65483.67
73263.86	56925.79
77303	69736.43
45437.85	49542.18
87699.3	71628.78
62488.01	91358.4
59655.36	52568.57
74263.75	72511.61
48196.33	56041.55
88239.42	80752.91
55734.81	75437.24
71213.24	51104.89
55639.66	65593.17
52482.21	46935.06
61645.62	97420.91
77602.12	97241.29
59728.99	86773.56
49463.04	77623.62
78049.64	64911.76