Question

A manufacturer of light bulbs claims that the average lifetime of one of their bulbs is more than 900 hours. A consumer advocacy group wants to test this claim. They obtained a simple random sample of 61 bulbs and timed how long they took to burn out. They obtained a sample mean of 907.5 hours with a standard deviation of 16.5 hours. It’s your job to test the claim at the 5% significance level and determine if the manufacturer is overstating the life of their bulbs or not.

Answer 1

Solution:

Given:

Claim: the average lifetime of one of their bulbs is more than 900 hours.

that is:

Sample size = n = 61

Sample mean =

Sample standard deviation = s = 16.5 hours

Significance level = 5% = 0.05

Step 1) State H0 and H1:

Vs  

This is right tailed ( one tailed) test.

Step 2) Test statistic:

Step 3) t critical value:

df = n -1 = 61 - 1 = 60

Significance level = 5% = 0.05

Look in t table for df = 61 and one tail area = 0.05 and find t critical value

t critical value = 1.671

Step 4) Decision Rule:

Reject null hypothesis H0, if t test statistic value > t critical value =1.671, otherwise we fail to reject H0

Since t test statistic value = > t critical value =1.671, we reject null hypothesis H0.

Step 5) Conclusion:

At 0.05 level of significance, we have sufficient evidence to support the manufacturer claim that the average lifetime of one of their bulbs is more than 900 hours.

Thus the manufacturer is not overstating the life of their bulbs.