Question

A company that manufactures light bulbs claims that its light bulbs last an average of 1500 hours. A consumer research group wants to test the hypothesis that the mean life of light bulbs manufactured by this company is less than 1500 hours. A sample of 35 light bulbs manufactured by this company gave a mean life of 1450 hours with a standard deviation of 100 hours. The significance level of the hypothesis test is 5% and the distribution for the population is known to be normally distributed.

When answering the questions below

• make sure a decimal representation begins with 0, like this: 0.286
• if a test has two Critical Values, type it like this: -2.34 & 2.34
• round z values to 2 decimal places, and t values to 3 decimal places
• for the result, type either Reject, or Fail to Reject

Please type in the Critical Value(s) , the Test Statistic , and the result of the test

Answer 1

Answer:

critical value T( critical) = 1.6909

Test statistics is t = -2.958

Conclusion:here we reject H0.

Explanation:

Here researcher wants to test the hypothesis that the mean life of light bulbs manufactured by this company is less than 1500 hours.

Hypothesis is:

H0: = 1500 verses H1: < 1500

Given :

sample mean = = 1450 , n = 35, sample standard deviation s = 100

The significance level of the hypothesis test is 5% i.e = 0.05

Hence the critical value for this test can be obtained from table with = 0.05 and df = n-1=35-1=34

T( critical) = 1.6909 ... (for one tailed)

Now Test statistics is

t = -2.958 ... rounded to 3 decimals

Conclusion:

We know that if |t| >T(critical) then we reject H0.

Here |t| = 2.958 > T( critical) = 1.6909 , hence we reject H0.