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 12 phones from the manufacturer had a mean range of 1070 feet with a standard deviation of 27 feet. A sample of 6 similar phones from its competitor had a mean range of 1050 feet with a standard deviation of 37 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 3 of 4 :

Determine the decision rule for rejecting the null hypothesis H0

. Round your answer to three decimal places.

Answer 1

Claim : the calling range (in feet) of its 900-MHz cordless telephone is greater than that of its leading competitor.

Hypothesis :

Given

n1 = 12

S1 = 27

n2 = 6

S2 = 37

Assumption variances are equal so we ise pooled t test:

Test Statistics :

T = 1.312

degrees of freedom

Df = n1+n2-2 = 12+6-2 = 16

P value = 0.104       

( p value we get using Excel =T.DIST.RT(1.312 ,16) )

p value 0.10 therefore we fails to reject H0.

Conclusion : There is not sufficient evidence to support the claim calling range (in feet) of its 900-MHz cordless telephone is greater than that of its leading competitor .