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 5 phones from the manufacturer had a mean range of 1180 feet with a standard deviation of 38 feet. a sample of 12 similar phones from its competitor had a mean range of 1120 feet with a standard deviation of 27 feet. do the results support the manufacturers claim? let $mu_1$ be the true mean range of the manufacturers cordless telephone and $mu_2$ be the true mean range of the competitors cordless telephone. use a significance level of $alpha = 0.1$ for the test. assume that the population variances are equal and that the two populations are normally distributed. step 1 of 4: state the null and alternative hypotheses for the test. answer 1 point $h_0:mu_1$ $mu_2$ $h_a:mu_1$ $mu_2$ = $
eq$ $>$ $<$ $geq$ $leq$

Explanation:

Step1: Understand the claim

The manufacturer claims that the calling - range of its cordless telephone is greater than that of its competitor. So, the alternative hypothesis should reflect this claim.

Step2: Define null and alternative hypotheses

The null hypothesis \(H_0\) is a statement of no effect or no difference. The alternative hypothesis \(H_a\) is what we are trying to find evidence for. Since the claim is that \(\mu_1>\mu_2\), the null hypothesis is \(H_0:\mu_1\leq\mu_2\) and the alternative hypothesis is \(H_a:\mu_1 > \mu_2\).

Answer:

\(H_0:\mu_1\leq\mu_2\), \(H_a:\mu_1 > \mu_2\)