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?

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, [tex]H_0[/tex] : p [tex]\leq[/tex] 0.50 {means that less than or equal to 50 percent of all young adults do not have a landline telephone number}

Alternate Hypothesis, [tex]H_a[/tex] : 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. = [tex]\frac{\hat p -p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)

where, [tex]\hat p[/tex] = % 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 = [tex]\frac{0.60-0.50}{\sqrt{\frac{0.60(1-0.60)}{1045} } }[/tex]

= 6.598

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