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 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.

Answer 1

a) H0: μ = 91,500 Ha: μ ≠ 91,500

b)

population mean μ=	91500
sample mean 'x̄=	85272.000
sample size   n=	25.00
sample std deviation s=	11039.230
std error 'sx=s/√n=	2207.846
test stat t ='(x-μ)*√n/sx=	-2.821

p value      =

0.0095

. Reject H0. We can conclude that the mean annual administrator salary in Ohio differs significantly from the national mean annual salary.

d)

H0: μ = 91,500 Ha: μ ≠ 91,500

test stat t ='(x-μ)*√n/sx=

-2.821

critical values for the rejection rule"

test statistic ≤-2.064

test statistic ≥2.064

Reject H0. We can conclude that the mean annual administrator salary in Ohio differs significantly from the national mean annual salary