## Among a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in school, 48%

Among a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in school, 48% said they decided not to go to college because they could not afford school.49 A newspaper article states that only a minority of the Americans who decide not to go to college do so because they cannot afford it and uses the point estimate from this survey as evidence. Conduct a hypothesis test to determine if these data provide strong evidence supporting this statement using the 7 steps and a significance level of 0.05.

## Answers ( )

Answer:Step-by-step explanation:We want to test hypothesis:

This is a lower tailed test

Sample proportion. =0.48, n= 331

And claimed proportion, P=0.5

Significance level, α=0.05 (if no value is given, we take level of 0.05)

Now, calculating statistics

Standard deviation of , =

=

0.0275

Test statistic,=

=

-0.727736

-0.73

Test statistic: -0.73

Since this is lower tailed test, p value = = P ( Z < -0.73) = 0.2327

p-value= 0.2327

note that exact p-value is : 0.2333875382

Rejection criteria : reject H0 if p-value <

Decision: Since, we fail to reject the null hypothesis. There is insufficient evidence to conclude that p is less than 0.5

Alternatively, we can use critical value approach,

(From z table, using interpolation, ½th distance between -1.64 and -1.65)

critical value = -1.645

Rejection criteria: Reject if

Decision : since , we fail to reject the null hypothesis. There is insufficient evidence to conclude that p is less than to 0.5