Consider the following competing hypotheses and accompanying sample data. Use Ta

Question

Consider the following competing hypotheses and accompanying sample data. Use Table 1 Ho P1-P220 HA P1 -P20 X1 224 1442 a. At the 10% significance level, find the critical value(s). (Negative values should be indicated by a X2-236 n2 = 442 minus sign. Round your answer to 2 decimal places.) Critical value b. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round all intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) Test statistic c. What is the conclusion? Reject Ho since the value of the test statistic is not less than the critical value Reject Ho since the value of the test statistic is less than the critical value. Do not reject Ho since the value of the test statistic is not less than the critical value. Do not reject Ho since the value of the test statistic is less than the critical value.

Explanation / Answer

The statistical software output for this problem is:

Two sample proportion summary hypothesis test:
p1 : proportion of successes for population 1
p2 : proportion of successes for population 2
p1 - p2 : Difference in proportions
H0 : p1 - p2 = 0
HA : p1 - p2 < 0

Hypothesis test results:

Hence,

a) Critical value = -1.28

b) Test statistic = -0.81

c) Option C is correct.

Difference Count1 Total1 Count2 Total2 Sample Diff. Std. Err. Z-Stat P-value p1 - p2 224 442 236 442 -0.027149321 0.033605738 -0.80787754 0.2096

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