Question

A survey of a random sample of 1,045 young adults found that 60 percent do not have a landline telephone number. A hypothesis test will be used to determine whether the data provide convincing statistical evidence that more than 50 percent of all young adults do not have a landline telephone number. What is the test statistic for the appropriate test?

Answer 1

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Answer 2

Answer:

Test statistic for the appropriate test is 6.598.

Step-by-step explanation:

We are given that a survey of a random sample of 1,045 young adults found that 60 percent do not have a landline telephone number.

We have to test the hypothesis that whether the data provide convincing statistical evidence that more than 50 percent of all young adults do not have a landline telephone number.

Let Null Hypothesis, $H_0$ : p $\leq$ 0.50  {means that less than or equal to 50 percent of all young adults do not have a landline telephone number}

Alternate Hypothesis, $H_a$ : p > 0.50  {means that more than 50 percent of all young adults do not have a landline telephone number}

The test statistics that will be used here is One-sample proportion test;

                T.S. = $\frac{\hat p -p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = % of young adults who do not have a landline telephone number

                      in a sample of 1,045 young adults = 60%

           n = sample of young adults = 1,045

So, test statistics =  $\frac{0.60-0.50}{\sqrt{\frac{0.60(1-0.60)}{1045} } }$

                            = 6.598

Hence, the test statistic for the appropriate test is 6.598.