You may need to use the appropriate technology to answer this question. Suppose the national mean annual salary for a school administrator is $91,500 a year. A school official took a sample of 25 school administrators in the state of Ohio to learn about salaries in that state to see if they differed from the national average. 77,600 76,000 90,700 97,200 90,700 101,800 78,700 81,300 84,200 97,600 77,500 75,700 89,400 84,300 78,700 84,600 87,700 103,400 83,800 101,300 94,700 69,200 95,400 61,500 68,800 (a) Formulate hypotheses that can be used to determine whether the population mean annual administrator salary in Ohio differs from the national mean of $91,500. H0: μ < 91,500 Ha: μ ≥ 91,500 H0: μ = 91,500 Ha: μ ≠ 91,500 H0: μ ≤ 91,500 Ha: μ > 91,500 H0: μ ≥ 91,500 Ha: μ < 91,500 H0: μ > 91,500 Ha: μ ≤ 91,500 (b) The sample data for 25 Ohio administrators is contained in the file named Administrator. What is the test statistic for your hypothesis test in part (a)? (Round your answer to three decimal places.) What is the p-value for your hypothesis test in part (a)? (Round your answer to four decimal places.) p-value = (c) At α = 0.05, can your null hypothesis be rejected? What is your conclusion? Do not reject H0. We can conclude that the mean annual administrator salary in Ohio differs significantly from the national mean annual salary.Reject H0. We can conclude that the mean annual administrator salary in Ohio differs significantly from the national mean annual salary. Do not reject H0. We cannot conclude that the mean annual administrator salary in Ohio differs significantly from the national mean annual salary.Reject H0. We cannot conclude that the mean annual administrator salary in Ohio differs significantly from the national mean annual salary. (d) Repeat the preceding hypothesis test using the critical value approach. State the null and alternative hypotheses. H0: μ < 91,500 Ha: μ ≥ 91,500 H0: μ = 91,500 Ha: μ ≠ 91,500 H0: μ ≤ 91,500 Ha: μ > 91,500 H0: μ ≥ 91,500 Ha: μ < 91,500 H0: μ > 91,500 Ha: μ ≤ 91,500 Find the value of the test statistic. (Round your answer to three decimal places.) State the critical values for the rejection rule. Use α = 0.05. (Round your answer to three decimal places. If the test is one-tailed, enter NONE for the unused tail.) test statistic≤test statistic≥ State your conclusion. Do not reject H0. We can conclude that the mean annual administrator salary in Ohio differs significantly from the national mean annual salary.Reject H0. We can conclude that the mean annual administrator salary in Ohio differs significantly from the national mean annual salary. Do not reject H0. We cannot conclude that the mean annual administrator salary in Ohio differs significantly from the national mean annual salary.Reject H0. We cannot conclude that the mean annual administrator salary in Ohio differs significantly from the national mean annual salary.

Question

DATAfile: Administrator

You may need to use the appropriate technology to answer this question.

Suppose the national mean annual salary for a school administrator is $91,500 a year. A school official took a sample of 25 school administrators in the state of Ohio to learn about salaries in that state to see if they differed from the national average.

77,600	76,000	90,700	97,200	90,700
101,800	78,700	81,300	84,200	97,600
77,500	75,700	89,400	84,300	78,700
84,600	87,700	103,400	83,800	101,300
94,700	69,200	95,400	61,500	68,800

(a)

Formulate hypotheses that can be used to determine whether the population mean annual administrator salary in Ohio differs from the national mean of $91,500.

H₀: μ < 91,500

H_a: μ ≥ 91,500

H₀: μ = 91,500

H_a: μ ≠ 91,500

H₀: μ ≤ 91,500

H_a: μ > 91,500

H₀: μ ≥ 91,500

H_a: μ < 91,500

H₀: μ > 91,500

H_a: μ ≤ 91,500

(b)

The sample data for 25 Ohio administrators is contained in the file named Administrator.

What is the test statistic for your hypothesis test in part (a)? (Round your answer to three decimal places.)

What is the p-value for your hypothesis test in part (a)? (Round your answer to four decimal places.)

p-value =

(c)

At

α = 0.05,

can your null hypothesis be rejected? What is your conclusion?

Do not reject H₀. We can conclude that the mean annual administrator salary in Ohio differs significantly from the national mean annual salary.Reject H₀. We can conclude that the mean annual administrator salary in Ohio differs significantly from the national mean annual salary. Do not reject H₀. We cannot conclude that the mean annual administrator salary in Ohio differs significantly from the national mean annual salary.Reject H₀. We cannot conclude that the mean annual administrator salary in Ohio differs significantly from the national mean annual salary.

(d)

Repeat the preceding hypothesis test using the critical value approach.

State the null and alternative hypotheses.

H₀: μ < 91,500

H_a: μ ≥ 91,500

H₀: μ = 91,500

H_a: μ ≠ 91,500

H₀: μ ≤ 91,500

H_a: μ > 91,500

H₀: μ ≥ 91,500

H_a: μ < 91,500

H₀: μ > 91,500

H_a: μ ≤ 91,500

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

State the critical values for the rejection rule. Use

α = 0.05.

(Round your answer to three decimal places. If the test is one-tailed, enter NONE for the unused tail.)

test statistic≤test statistic≥

State your conclusion.

Do not reject H₀. We can conclude that the mean annual administrator salary in Ohio differs significantly from the national mean annual salary.Reject H₀. We can conclude that the mean annual administrator salary in Ohio differs significantly from the national mean annual salary. Do not reject H₀. We cannot conclude that the mean annual administrator salary in Ohio differs significantly from the national mean annual salary.Reject H₀. We cannot conclude that the mean annual administrator salary in Ohio differs significantly from the national mean annual salary.