Question

The nationwide percentage of Americans who invest in the stock market is usually taken to be 55%. Is this percentage different in the state of Ohio? A random sample of 76 Ohio residents were sampled and asked whether they invest in the stock market. 57.3% (or 0.573 as a decimal) responded that they do invest in the stock market. Here, the parameter of interest is p, the proportion of Ohioans who invest in the stock market, and we are testing H0: p = 0.55 versus the alternative Ha: p ≠ 0.55. What is the p-value for this two-tailed test?

Less than 0.05

Between 0.05 and 0.10

Between 0.10 and 0.25

Between 0.25 and 0.50

Greater than 0.50

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.55

H_a : p 0.55

= 0.573

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.573 - 0.55 / [(0.55 * 0.45) / 76]

= 0.403

P-value = 0.6869

The p-value for this two-tailed test is :

Greater than 0.50