Question

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Use either the critical value method or the P-value method as indicated. Identify the null and alternative hypotheses, test statistic, critical value(s) or P-value (or range of P-values) as appropriate, and state the final conclusion that addresses the original claim. A light-bulb manufacturer advertises that the average life for its light bulbs is 900 hours. A random sample of 15 of its light bulbs resulted in the following lives in hours. 995 590 510 539 739 917 571 555 916 728 664 693 708 887 849 At the 10% significance level, test the claim that the sample is from a population with a mean life of 900 hours. Use the P-value method of testing hypotheses.

Answer 1

We need to find the mean and standard deviation of the given data

Since we know that

Where n is the number of data points

Now

and n = 15

This implies that

Since we know that

The test hypothesis is

This is a two-sided test because the alternative hypothesis is formulated to detect differences from the hypothesized mean value of 30 on either side.

Now, the value of test static can be found out by following formula:

Using Excel's function =, the P-value for t0 = -4.3422 in an t-test with 14 degrees of freedom can be computed as

We would reject the null hypothesis in favor of the alternative hypothesis because P = 0.00068<0.1

For .

Since t_0 = -4.3422 < -1.7613 = -t_{0.05}, we reject the null hypothesis in favor of the alternative hypothesis at .