Question

In 2008, 58% of adults in a certain country had a college education. A researcher suspects that the percent is higher now. She obtains a random sample of 1012 adults and finds that 590 have a college education. Is this sufficient evidence to support the researcher’s claim at the 10% level of significance? Your answer should show all four steps of the hypothesis test.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H0 : p = 0.58

Ha : p > 0.58

$\hat p$ = x / n = 590 / 1012 = 0.583

P0 = 0.58

1 - P0 = 1 - 0.58 = 0.42

Test statistic = z

= $\hat p$ - P0 / [$\sqrt$P0 * (1 - P0 ) / n]

= 0.583 - 0.58 / [$\sqrt$(0.58 * 0.42) / 1012]

= 0.19

P(z > 0.19) = 1 - P(z < 0.19) = 1 - 0.5753

P-value = 0.4247

$\alpha$ = 0.10

P-value > $\alpha$

Fail to reject the null hypothesis .

There is not sufficient evidence to support the researcher’s claim