Question

Suppose that you were trying to determine if the population proportion of Americans that currently believe that nuclear power is extremely/very dangerous to the environment was less than 50%. You decide to test the null hypothesis Ho: p = 0.50 versus Ha: p < 0.50.

In 2010, the General Social Survey included a question that asked its participants if they felt that nuclear power plants were extremely/very dangerous to the environment. Out of the 1340 surveyed, 634 said yes. What is the value of the test statistic for this problem?

0.975

-0.975

1.97

-1.97

Answer 1

Solution :

This hypothesis test is a left tailed test .  

The null and alternative hypothesis is

H₀ : p = 0.50

H_a : p < 0.50

$\hat p$ = x / n = 634 / 1340 = 0.4731

1 - P₀ = 1 - 0.50 = 0.5

Test statistic = z

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

= 0.4731 - 0.50 / [$\sqrt$(0.50 (0.5)) / 1340]

= -1.97

The test statistic is -1.97