Question

Suppose that we are to conduct the following hypothesis test:

H0: μ=990

H1:μ>990

Suppose that you also know that σ=220, n=100, x¯=1031.8, and take α=0.01.

Draw the sampling distribution, and use it to determine each of the following:

A. The value of the standardized test statistic:

Note: For the next part, your answer should use interval notation.

An answer of the form (−∞,a) is expressed (-infty, a), an answer of the form (b,∞) is expressed (b, infty), and an answer of the form (−∞,a)∪(b,∞) is expressed (-infty, a)U(b, infty).

B. The rejection region for the standardized test statistic:

C. The p-value is

D. Your decision for the hypothesis test:

A. Reject H1.

B. Do Not Reject H1.

C. Reject H0.

D. Do Not Reject H0.

Answer 1

Solution :

Test statistic = z

= ( - ) / / n

= (1031.8 - 990) /220 / 100

= 1.9

Test statistic = 1.9

Z_0.01 = 2.326

Z > 2.326

This is the right tailed test .

P(z > 1.9) = 1 - P(z < 1.9) = 0.0287

P-value = 0.0287

= 0.01

P-value >

Fail to reject the H0