Question

20. Large Sample Proportion Problem. Surveys were conducted in multiple countries and respondents were asked if they felt political news was reported fairly. The data for the United States is that out of 1,000 sampled, 470 indicated yes, they felt political news was reported fairly. Suppose we want to determine if the proportion for the U.S. is below .50 for an alpha level of .05.

What is the conclusion of my test?

A. I would reject Ho: P=.5 because the test statistic is greater than 1.645

B. I would fail to reject Ho: P=.5 because the p-value is greater than .05

C. I would reject Ho: P=.5 because the test statistic is less than -1.645

D. I would fail to reject Ho: P=.5 because the test statistic is greater than -1.96

Answer 1

H₀: P = 0.50

H₁: P < 0.50

= 470/1000 = 0.47

The test statistic z = ( - P)/sqrt(P(1 - P)/n)

                             = (0.47 - 0.5)/sqrt(0.5 * 0.5/1000)

                             = -1.90

At alpha = 0.05, the critical value is z_0.05 = -1.645

Since the test statistic value is less than the critical value(-1.90 < -1.645), so we should reject the null hypothesis.

Option - C) I would reject H₀: P = 0.5, because the test statistic is less than -1.645.