Question

A manufacturer of light bulbs advertises that, on average, its long-life bulb will last more than 5100 hours. To test this claim, a statistician took a random sample of 98 bulbs and measured the amount of time until each bulb burned out. The mean lifetime of the sample of bulbs is 5156 hours and has a standard deviation of 390 hours. Can we conclude with 99% confidence that the claim is true? Fill in the requested information below.

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

B. The rejection region for the standardized test statistic:

C. The p-value is

D. Your decision for the hypothesis test:

A. Reject H0.
B. Reject H1.
C. Do Not Reject H1.
D. Do Not Reject H0.

Answer 1

from above

A) value of the standardized test statistic =1.42

b) rejection region for the standardized test statistic (2.33 , inf).

c)p value =0.0778

d) D. Do Not Reject H0