Question

Suppose eduaction dept of New York State is contemplating whether the state of Ny Receives a significantly different amount of public school funding (per student) than the USA average. They find that the USA mean public school yearly funding is $6800per student per year with a standard deviation of $400. Suppose the dept collects a sample (n=100) from ny and determines that the sample mean for NY (per student, per year) is $6873. Use the z test to run a hypothesis test to determine if NY receives a significantly different amount of funding fror public school education (per student per year. 1. what are the null and alternative hypothesis here? 2. Assuming confidence level of 95%, determine the alpha and critical value. 3. Determine whether a left tailed, right tail or two tailed test is performed. 4. Calculate the t test statistics or the z test. 5. Compare the test statistics score with the critical value. Depict your reslts graphhically. 6. Determine whether the null hypothesis is rejected or not?

Answer 1

x̅ = 6873, σ = 400, n = 100

1) Null and Alternative hypothesis:

Ho : µ = 6800

H1 : µ ≠ 6800

2) α = 1-0.95 = 0.05

Critical value :

Two tailed critical value, z crit = ABS(NORM.S.INV(0.05/2)) = +/- 1.960

Reject Ho if z < -1.96 or if z > 1.96

3. It is a two tailed test.

4. Test statistic:

z = (x̅- µ)/(σ/√n) = (6873 - 6800)/(400/√100) = 1.8250

5. Graph:

ZC = -1.96 20-1,96 zc = 1.96 = 1.82513 3 2 1 ó z = 1.825 i

6. Decision:

Do not reject the null hypothesis.