Question

A manufacturer claims that the calling range (in feet) of its 900-MHz cordless telephone is greater than that of its leading competitor. A sample of 13 phones from the manufacturer had a mean range of 1090 feet with a standard deviation of 21 feet. A sample of 9 similar phones from its competitor had a mean range of 1030 feet with a standard deviation of 42 feet. Do the results support the manufacturer's claim? Let μ1 be the true mean range of the manufacturer's cordless telephone and μ2 be the true mean range of the competitor's cordless telephone. Use a significance level of α=0.05 for the test. Assume that the population variances are equal and that the two populations are normally distributed.

Step 2 of 4 : Compute the value of the t test statistic. Round your answer to three decimal places.

Step 3 of 4: Determine the decision rule for rejecting the null hypothesis H0. Round your answer to three decimal places.

Step 4 of 4: State the test's conclusion.

Answer 1

The statistic software output for this problem is:

sample T summary hypothesis test: Mean of Population 1 H2 Mean of Population 2 H1 2 Difference between two means Ho H-20 HA -2 0 (with pooled variances) Hypothesis test results: Difference Sample Diff. Std. Err. DF T-Stat P-value 60 13.506693 20 4.4422419 0.0001

the t test statistic = 4.442

Critical value = 1.725

Test statistics < critical value

Reject the null hypothesis