You wish to test the following claim (HaHa) at a significance level of α=0.05.      Ho:p1=p2      Ha:p1<p2You obtain 87.4% successes in a sample of size n1=452 from the first population. You obtain 95.3% successes in a sample of size n2=633 from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution.What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.)p-value =

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Asked Nov 25, 2019
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You wish to test the following claim (HaHa) at a significance level of α=0.05.

      Ho:p1=p2
      Ha:p1<p2

You obtain 87.4% successes in a sample of size n1=452 from the first population. You obtain 95.3% successes in a sample of size n2=633 from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution.

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic = 

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value = 

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Expert Answer

Step 1

Null Hypothesis:

 

H0:p1=p2

 

Alternative Hypothesis:

 

H1:p1<p2

Step 2

Test Statistic:

 

From the given information, there are 87.4% successes in a sample of n1=452 and there are 95.3% successes in a sample of n2=633. That is, p1=0.874, p2=0.953,  n1=452 and n2=633.

 

The pooled sample proportion is,

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(452x 0.874)+(633 x 0.953) 452 633 0.920

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Step 3

The test statistic is -4.729 and it is c...

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test 1 P(1-p) п п, п, 0.874-0.953 1 0.920(1-0.920) 452 633 -0.079 0.016706 =-4.729 Il

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Hypothesis Testing

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