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 9 phones from the manufacturer had a mean range of 1180 feet with a standard deviation of 35 feet. A sample of 15 similar phones from its competitor had a mean range of 1120 feet with a standard deviation of 20 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=0.1 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 1 of 4: State the null and alternative hypotheses for the test.

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

Step 1 of 4

Null Hypothesis : H₀ : There is no difference in true mean range of manufacturer's cordless teleophoneand true mean range of the competitor's cordless telephone.

Alternative Hypothesis : H_a : THere is significant difference in the true mean range  of manufacturer's cordless teleophoneand true mean range of the competitor's cordless telephone.

Step 2 of 4

Pooled standard deviation = sqrt [{(n₁ -1)s₁² + (n₂ -1)s₂²}/(n₁ + n₂ -2)]

= sqrt [(8 * 35² + 14 * 20²)/(8 + 14)] = 26.4575

Test statistic

t = ()/ sqrt [ s²_p * (1/n₁ + 1/n₂)]

= (1180 - 1120)/ sqrt [26.4575 * (1/9 + 1/15)]

= 60/ 11.155 = 5.378

Step 3 of 4

Here critical value of test statistic for t_critical = 2.074

so here

t > t_critical so we will reject the null hypothesis .

p - value = Pr(t > 5.378 ; 22) = 0.000002

Step 4 : 4

THere is significant difference in the true mean range  of manufacturer's cordless teleophoneand true mean range of the competitor's cordless telephone.