Question

A survey of a random sample of 1,045 young adults found that 60 percent do not have a landline telephone number. Test statistic of the appropriate test?

Answer 1

The test statistic value = 6.49

Explanation:

Given Data;

n = 1045

P = 0.6

the null and alternative hypotheses can be defined as:

H0 : P = 0.50

H1 : p greater than 0.50

The test statistic value is calculated using the formula;

z = (P - Po)/(√Po(1-Po)/n)

Substituting, we have

z = (0.60 - 0.50)/(√0.50(1-0.50)/1045)

z = 0.1/(√0.5*0.5)/1045)

= 0.1/√0.000239

= 0.1/0.0154

= 6.49

Note: The test statistic will be used to make decision about the hypothesis test.

Answer 2

6.598

Explanation:

- A random sample of n = 1,045 young adults found that 60 % do not have a landline telephone number.

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

- Let Null Hypothesis, H_o: p 0.50

- Alternate Hypothesis, H_1 : p > 0.50

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

Test =
`\frac{p' - p}{\sqrt{(p'*(1 - p'))/(n) } }` ~ N(0,1)

- Where, p' = % of young adults who do not have a landline telephone number in a sample of n is = 60%

- Where, n = sample of young adults = 1,045

- So, test statistics =
`\frac{0.6 - 0.5}{\sqrt{(0.6*(1 - 0.6))/(1045) } }` = 6.598

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