Question

A report stated that 29% of the people in a representative sample of adult Americans ages 33 to 49 rated a landline telephone among the three most important services that they purchase for their home. In a representative sample of adult Americans ages 50 to 68, 44% rated a landline telephone as one of the top three services they purchase for their home. Suppose that the samples were independently selected and that the sample size was 590 for the 33 to 49 age group sample and 610 for the 50 to 68 age group sample. Does this data provide convincing evidence that the proportion of adult Americans ages 33 to 49 who rate a landline phone in the top three is less than this proportion for adult Americans ages 50 to 68? Test the relevant hypotheses using

α = 0.05.

(Use p_{33 to 49 age group} − p_{50 to 68 age group}.)

Find the test statistic. (Round your answer to two decimal places.)

Answer 1

p-value ~ 0 < 0.05 i.e. we can reject H0 and hence we can conclude that the proportion of adult Americans ages 33 to 49 who rate a landline phone in the top three is less than this proportion for adult Americans ages 50 to 68.

Note: Calculations are a bit off but not by much. So if you want exact calculations just input the values in the z-statistic formula. The conclusion is right though.

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