Conduct the following test at the a 0.01 level of significance by determining (a) the null and alternative hypotheses, (b) the test statistic, and (c) the P-value. Assume that the samples were obtained independently using simple random sampling.Test whether p1 #p2. Sample data are x1 30, n, 254, x2 =38, and n2 = 301(a) Determine the null and alternative hypotheses. Choose the correct answer belowA. Ho: p1 0 versus H1: p = 0B. Ho: P1 p2 versus H1: p1 >P2D. Ho: p1 P2 versus H4: p1 P2C. Do not reject the null hypothesis because there is sufficient evidence to conclude thatP1D. Do not reject the null hypothesis because there is not sufficient evidence to conclude that p p2

Question
Asked Oct 21, 2019
Conduct the following test at the a 0.01 level of significance by determining (a) the null and alternative hypotheses, (b) the test statistic, and (c) the P-value. Assume that the samples were obtained independently using simple random sampling.
Test whether p1 #p2. Sample data are x1 30, n, 254, x2 =38, and n2 = 301
(a) Determine the null and alternative hypotheses. Choose the correct answer below
A. Ho: p1 0 versus H1: p = 0
B. Ho: P1 p2 versus H1: p1 >P2
D. Ho: p1 P2 versus H4: p1 <P2
C. Ho: p1 P2 versus H1: p1 # P2
(b) The test statistic
is
(Round to two decimal places as needed.)
Zo
(c) The P-value is
(Round to three decimal places as needed.)
Test the null hypothesis. Choose the correct conclusion below
A. Reject the null hypothesis because there is sufficient evidence to conclude that p p2
B. Reject the null hypothesis because there is not sufficient evidence to conclude that p
<p2
>P2
C. Do not reject the null hypothesis because there is sufficient evidence to conclude that
P1
D. Do not reject the null hypothesis because there is not sufficient evidence to conclude that p p2
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Conduct the following test at the a 0.01 level of significance by determining (a) the null and alternative hypotheses, (b) the test statistic, and (c) the P-value. Assume that the samples were obtained independently using simple random sampling. Test whether p1 #p2. Sample data are x1 30, n, 254, x2 =38, and n2 = 301 (a) Determine the null and alternative hypotheses. Choose the correct answer below A. Ho: p1 0 versus H1: p = 0 B. Ho: P1 p2 versus H1: p1 >P2 D. Ho: p1 P2 versus H4: p1 <P2 C. Ho: p1 P2 versus H1: p1 # P2 (b) The test statistic is (Round to two decimal places as needed.) Zo (c) The P-value is (Round to three decimal places as needed.) Test the null hypothesis. Choose the correct conclusion below A. Reject the null hypothesis because there is sufficient evidence to conclude that p p2 B. Reject the null hypothesis because there is not sufficient evidence to conclude that p <p2 >P2 C. Do not reject the null hypothesis because there is sufficient evidence to conclude that P1 D. Do not reject the null hypothesis because there is not sufficient evidence to conclude that p p2

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Expert Answer

Step 1

The provided information is as follows:

0.01
x 30
n 254
x 38
n2 301
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0.01 x 30 n 254 x 38 n2 301

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Step 2

a) Null hypothesis state that there is no significant difference between two specified populations.

Alternative hypothesis state that there is no significant difference between two specified populations.

In this case, in order to test the p1≠p2, the hypothesis is defined as:

Но : р. 3 р.
Н: р. # Р.
Therefore option C is correct
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Но : р. 3 р. Н: р. # Р. Therefore option C is correct

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Step 3

b) Consider  and  are two sample proportion. The z score t...

(р - Р.) -0
Z =
1
1
1-p)
п
п,
Here p is a pooled sample proportion which can be calculated as:
((Р. хп)+(р, хт))
п +п,
((0.118x254)+(0.126x301))
555
= 0.122
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(р - Р.) -0 Z = 1 1 1-p) п п, Here p is a pooled sample proportion which can be calculated as: ((Р. хп)+(р, хт)) п +п, ((0.118x254)+(0.126x301)) 555 = 0.122

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