Question

A company manufacturing light bulbs is testing a new model. The company claims that the mean life time is less than 1000 hours.

A sample of 16 light bulbs are found to have sample mean of 987.5 hours and a sample variance of 400.

(a) Test this claim at the significance level α = 0.02.

Answer 1

Answer: A company manufacturing light bulbs is testing a new model. The company claims that the mean life time is less than 1000 hours. A sample of 16 light bulbs are found to have sample mean of 987.5 hours and a sample variance of 400.

(a) Test this claim at the significance level α = 0.02.

Solution:

n = 16

x̄ = 987.5

Variance = 400

Standard deviation s = √variance

s = √400

s = 20

The hypothesis test:

Ho: μ = 1000

Ha: μ < 1000

Test statistic t:

t = x̄ - μ / s / √n

t = 987.5 - 1000 / 20 / √16

Test statistic t = - 2.5

P-value:

P-value from test statistic and df at α = 0.02 significance level.

df = n-1 = 16 -1 = 15

P-value = 0.0123

Since, P-value (0.0123) < α (0.02) significance level.

Reject the null hypothesis Ho.

There is sufficient evidence to support the claims that the mean life time is less than 1000 hours.