Question

(1 point) Suppose that you are to conduct the following hypothesis test:

H0:H1:μμ=≠510510H0:μ=510H1:μ≠510

Assume that you know that σ=90σ=90, n=42n=42, x¯=487.5x¯=487.5, and take α=0.1α=0.1. 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)(−∞,a) is expressed (-infty, a), an answer of the form (b,∞)(b,∞) is expressed (b, infty), and an answer of the form (−∞,a)∪(b,∞)(−∞,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. Do Not Reject H0H0.
B. Reject H1H1.
C. Do Not Reject H1H1.
D. Reject H0H0.

Answer 1

H0: = 510 , Ha: 510

A)

Test statistics

z = - / ( / sqrt(n) )

= 487.5 - 510 / ( 90 / sqrt(42) )

= -1.62

B)

At 0.1 significance level, critical value is -1.645 , 1.645

Rejection region - reject H0 if test statistics z < -1.645 of test statistics z > 1.645

C)

p-value = 2 * P( Z < z)

= 2 * P( Z < -1.62)

= 2 * ( 1 - P( Z < 1.62) )

= 2 * ( 1 - 0.9474 )

= 0.1052

D)

Since test statistics value falls in non rejection region that is falls in -1.645 and 1.645, we do not have

sufficient evidence to reject H0.

Do not reject H0