Question

A manufacturer of light bulbs advertises that, on average, its long-life bulb will last more than 5500hours. To test this claim, a statistician took a random sample of 90 bulbs and measured the amount of time until each bulb burned out. The mean lifetime of the sample of bulbs is 5551 hours and has a standard deviation of 420 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:

(b) The rejection region for the standardized test statistic:

(c) Your decision for the hypothesis test:

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

Answer 1

Answer

(A) given that

sample mean (xbar) = 5551

standard deviation (s) = 420

sample size n = 90

population mean (mu) = 5500

test statistic =

$(\bar{x}-\mu)/(s/\sqrt{n}) \\ = (5551-5500)/(420/\sqrt{90}) \\ = 51/42.2719 \\ = 1.15$

(B) degree of freedom = n-1

= 90-1

= 89

alpha level = 1 -confidence level = 1-0.99 = 0.01

using t distribution table with alpha(0.01) and df(89)

we get

t critical = -2.37

We will reject Ho when test statistic is less than -2.37

(C) since test statistic is not less than -2.37, so we failed to reject the Ho

option B