Test whether he given claim is supported or not supported using a 0.05 significance level. Assume that the sample has been randomly selected from a population with a normal distribution.
-A manufacturer claims that the mean lifetime of its fluorescent bulbs is 1300 hours. A product tester selects 25 bulbs and finds the mean lifetime to be 1280 hours with a standard deviation of 80 hours. He claims that the mean lifetime is different from 1300 hours. Use a significance level of 0.05 to test whether the product tester's claim is supported or not supported.
A)supported
B)not supported

Question

Quizplus · Accepted Answer

The null hypothesis is that the mean lifetime is 1300 hours. The alternative hypothesis is that the mean lifetime is different from 1300 hours. Using a t-test for the sample mean, the test statistic is calculated as (1280 - 1300) / (80/√25) = -1.25. The critical t-value for a two-tailed test with 24 degrees of freedom at a 0.05 significance level is approximately ±2.064. Since -1.25 is within the range of -2.064 to 2.064, we fail to reject the null hypothesis. Therefore, the product tester's claim is not supported.

Test Whether He Given Claim Is Supported or Not Supported