Question

In 2011, a U.S. Census report determined that 71% of college students work. A researcher thinks this percentage has changed since then. A survey of 110 college students reported that 91 of them work. Is there evidence to support the reasearcher's claim at the 1% significance level? A normal probability plot indicates that the population is normally distributed. a) Determine the null and alternative hypotheses. Ho: p = H:P Select an answer (Put in the correct symbol and value) b) Determine the test statistic. Round to two decimals. c) Find the p-value. Round to 4 decimals. P-value =

Answer 1

Solution :

This is the two tailed test .

a) The null and alternative hypothesis is

H₀ : p = 0.71

H_a : p $\neq$ 0.71

$\hat p$ = x / n = 91/110 = 0.83

1 - P₀ = 1 - 0.71 = 0.29

b) Test statistic = z

= $\hat p$ - P₀ / [$\sqrt$P_{0 *} (1 - P₀ ) / n]

= 0.83 - 0.71 / [$\sqrt$(0.71 * 0.29) / 110]

= 0.12‬ / 0.043265

Test statistic = 2.77

c) P-value

P(z > 2.77) = 2 * [1 - P(z < 2.77)] = 2 * 0.0028‬

P-value = 0.0056‬

$\alpha$ = 0.01

P-value < $\alpha$

Reject the null hypothesis .

There is sufficient evidence to support the researchers claim at the 1% significance level.