Question

Use the following to answer questions a-d: In an August 2012 Gallup survey of 1,012 randomly selected U.S. adults (age 18 and over), 53% said that they were dissatisfied with the quality of education students receive in kindergarten through grade 12. Test, at the 5% level, if this sample provides evidence that the proportion of Americans who are dissatisfied with education in kindergarten through grade 12 differs significantly from 50%.

a. State the null and alternative hypothesis.

b. Verify that it is appropriate to use a normal distribution to compute the p-value

c. Calculate the Test statistic

d. Use Statkey to find the p-value.

e. Make a formal decision about the test.

f. What conclusion can you make in context of this problem.

Answer 1

a) H₀: P = 0.5

    H₁: P 0.5

b) np₀(1 - p₀) = 1012 * 0.5 * 0.5 = 253

Since np₀(1 - p₀) > 10, so we can use normal approximation to the proportion.

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

                                 = (0.53 - 0.5)/sqrt(0.5 * 0.5/1012)

                                 = 1.91

d) P-value = 2 * P(Z > 1.91)

                 = 2 * (1 - P(Z < 1.91))

                 = 2 * (1 - 0.9719)

                 = 0.0562

e) Since the P-value is greater than the significance level(0.0562 > 0.05), so we should not reject the null hypothesis.

f) At 5% level of significance, there is not sufficient evidence to conclude that the proportion of Americans who are dissatisfied with education in kindergarten through grade 12 differs significantly from 50%.