Consider the following competing hypotheses and accompanying sample data. Use Ta
ID: 3160652 • Letter: C
Question
Consider the following competing hypotheses and accompanying sample data. Use Table 1. H_0: P_1-P_2 = 0.04 H_A: P_1- P_2 0 04 X_1 = 125 x_2 = 143 n_1 = 271 n_2 = 446 Calculate the value of the test statistic. (Round intermediate calculations to 4 decimal places and final answer to 2 decimal places.) Test statistic -2.69 Calculate the p-value. (Round your answer to 4 decimal places.) p-value 0.0071 At the 1% significance level, what is the conclusion? Reject H_0; the population proportions do not differ by 0.04. Using the critical value approach, can we reject the null hypothesis at the 1 % level? Yes since the value of the test statistic is more than the critical value Of 2,316.Explanation / Answer
A)
Formulating the hypotheses
Ho: p1 - p2 = 0.04
Ha: p1 - p2 =/= 0.04
Here, we see that pdo = 0.04 , the hypothesized population proportion difference.
Getting p1^ and p2^,
p1^ = x1/n1 = 0.461254613
p2 = x2/n2 = 0.320627803
Also, the standard error of the difference is
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] = 0.037488238
Thus,
z = [p1 - p2 - pdo]/sd = 2.684223536 = 2.68 [ANSWER, TEST STATISTIC]
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b)
Also, the p value is, as this is two tailed,
P = 0.0037*2 = 0.0074 [ANSWER]
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c)
As P < 0.01,
Reject Ho. The population proportions do not differ by 0.04. [ANSWER]
[Option C has to be correct. Please report this part to your instructor.]
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d)
As it is 0.01 level, two tailed, then
zcrit = 2.576.
Hence,
Yes, since the value of the test statistic is more than the critical value of 2.576. [ANSWER]
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