Question

According to a study by the American Pet Food Dealers Association, 42% of U.S. households own pets. A report is being prepared for an editorial in the San Francisco Chronicle. As a part of the editorial a random sample of 265 households showed 175 own pets. Does this data disagree with the Pet Food Dealers Association data? Use a 0.20 level of significance. (a) State the null hypothesis and the alternate hypothesis. (b) State the decision rule for 0.20 significance level. (Negative value should be indicated by a minus sign. Round your answers to 2 decimal places.) (c) Compute the value of the test statistic. (Round your answer to 2 decimal places.) (d) Does this data disagree with the Pet Food Dealers Association data? Use a 0.20 level of significance. H0 is (_____). There is (____) evidence to show the proportion has changed.

Answer 1

a) H₀: P = 0.42

H₁: P 0.42

b) At alpha = 0.20, the critical values are z_0.1 = +/- 1.28

Reject H₀, if z < -1.28, or, z > 1.28

c) = 175/265 = 0.6604

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

                             = (0.6604 - 0.42)/sqrt(0.42 * (1 - 0.42)/265)

                             = 7.93

Since the test statistic value is greater than the positive critical value(7.93 > 1.28), so we should reject the null hypothesis.

H₀is rejected. There is sufficient evidence to show the proportion has changed.