Question

Find the sample proportions and test statistic for equal proportions. (a-1) Dissatisfied workers in two companies: x1 = 46, n1 = 100, x2 = 36, n2 = 100, α = .05, two-tailed test. (Round your answers to 4 decimal places. Use Excel to calculate the p-value.) p1 p2 zcalc p-value zα/2 +/- (a-2) Choose the appropriate hypotheses. a. H0:π1 – π2 = 0 vs. H1:π1 – π2 ≠ 0. Reject H0 if zcalc < –1.96 or zcalc > 1.96 b. H0:π1 – π2 = 0 vs. H1:π1 – π2 ≠ 0. Reject H0 if zcalc > –1.96 or zcalc < 1.96 a b (a-3) Based on the data reject H0. False True (b-1) Rooms rented at least a week in advance at two hotels: x1 = 30, n1 = 200, x2 = 18, n2 = 50, α = .01, left-tailed test. (Round your answers to 4 decimal places. Negative values should be indicated by a minus sign. Use Excel to calculate the p-value.) p1 p2 zcalc p-value zα (b-2) Choose the appropriate hypotheses. a. H0:π1 – π2 ≥ 0 vs. H0:π1 – π2 < 0. Reject H0 if zcalc > 2.3263 b. H0:π1 – π2 ≥ 0 vs. H0:π1 – π2 < 0. Reject H0 if zcalc < –2.3263 a b (b-2) Based on the data reject H0. True False (c-1) Home equity loan default rates in two banks: x1 = 42, n1 = 480, x2 = 32, n2 = 520, α = .05, right-tailed test. (Round your answers to 4 decimal places. Use Excel to calculate the p-value.) p1 p2 zcalc p-value zα (c-2) Choose the appropriate hypotheses. a. H0:π1 – π2 ≤ 0 vs. H1:π1 – π2 > 0. Reject H0 if zcalc > 1.645 b. H1:π1 – π2 ≤ 0 vs. H1:π1 – π2 > 0. Reject H0 if zcalc < 1.645 a b (c-3) Based on the data reject H0. True False

Answer 1

1. From the given data

Correct answer:  Reject H0 if zcalc < –1.96 or zcalc > 1.96

Here P-value is > alpha 0.05 so we accept H0

Thus we conclude that :π1 – π2 = 0

2. Correct answer: Reject H0 if zcalc < –2.3263

From the given data

Here P-value = 0.0004 < alpha 0.01 so we reject H0

thus we conclude that π1 – π2 < 0.

3.

Correct answer: Reject H0 if zcalc > 1.645

Here P-value > alpha 0.05 so we reject H0 i.e. π1 – π2 > 0