Question

Suppose that we are to conduct the following hypothesis test:

H0:μ=1010

H1:μ>1010

Suppose that you also know that σ=250, n=95, x¯=1067.5, 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. Do Not Reject H1.

B. Reject H1.

C. Reject H0.

D. Do Not Reject H0.

Answer 1

a)

population std dev ,    σ =    250.0000                  
Sample Size ,   n =    95                  
Sample Mean,    x̅ =   1067.5000                  
                          
'   '   '                  
                          
Standard Error , SE = σ/√n =   250.0000   / √    95   =   25.6495      
Z-test statistic= (x̅ - µ )/SE = (   1067.500   -   1010   ) /    25.6495   =   2.242

b)

critical z value, z* =       2.3263

rejection region: (2.3263, inf)

c)

p-Value   =   0.0125   [ Excel formula =NORMSDIST(-z) ]

d)

D. Do Not Reject H0.