Question

According to a survey in PARADE magazine, almost half of parents say their children's weight is fine. Only 9% of parents describe their children as overweight.† However, the American Obesity Association says the number of overweight children and teens is at least 15%. Suppose that you sample n = 650 parents and the number who describe their children as overweight is x = 55.

(a)

How would you test the hypothesis that the proportion of parents who describe their children as overweight is less than the actual proportion reported by the American Obesity Association? (Round your answers to two decimal places.)

State the null and alternative hypotheses.

H₀: p ? 0.15 versus H_a: p < 0.15

H₀: p = 0.15 versus H_a: p < 0.15

    

H₀: p ? 0.09 versus H_a: p < 0.09

H₀: p = 0.15 versus H_a: p > 0.15

H₀: p = 0.09 versus H_a: p > 0.09

Find the test statistic and rejection region. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.)

test statisticz=rejection regionz>z<

(b)

What conclusion are you able to draw from these data at the ? = 0.05 level of significance?

H₀ is not rejected. There is insufficient evidence to indicate that the proportion of parents who describe their children as overweight is less than the actual proportion reported by the American Obesity Society.H₀ is rejected. There is sufficient evidence to indicate that the proportion of parents who describe their children as overweight is less than the actual proportion reported by the American Obesity Society.    H₀ is not rejected. There is sufficient evidence to indicate that the proportion of parents who describe their children as overweight is less than the actual proportion reported by the American Obesity Society.H₀ is rejected. There is insufficient evidence to indicate that the proportion of parents who describe their children as overweight is less than the actual proportion reported by the American Obesity Society.

(c)

What is the p-value associated with this test? (Round your answer to four decimal places.)

p-value =

Answer 1

a) H₀: P = 0.15

   H_a: P < 0.15

p = 55/650 = 0.0846

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

                             = (0.0846 - 0.15)/sqrt(0.15 * (1 - 0.15)/650)

                             = -4.67

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

Rejection region is z < -1.645

b) Since the test statistic value is less than the critical value (-4.67 < -1.645), so the null hypothesis is rejected.

H₀ is rejected. There is sufficient evidence to indicate that the proportion of parents who describe their children as overweight is less than the actual proportion reported by the American Obesity Society.

c) P-value = P(Z < -4.67)

                 = 0.0000