A hospital administrator claims that the proportion of knee surgeries that are successful is 87%. To test this claim, a random sample of 450 patients who underwent knee surgery is taken and it is determined that 371 of these patients had a successful knee surgery operation. The following is the setup for this hypothesis test: {H0:p=0.87Ha:p≠0.87 Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places.

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Asked Oct 1, 2019
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A hospital administrator claims that the proportion of knee surgeries that are successful is 87%. To test this claim, a random sample of 450 patients who underwent knee surgery is taken and it is determined that 371 of these patients had a successful knee surgery operation. 

The following is the setup for this hypothesis test:

 

{H0:p=0.87Ha:p≠0.87

 

Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places.

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Expert Answer

Step 1

The hypotheses are given below:

Null hypothesis: H0:p=0.87

Alternative hypothesis: Ha:p≠0.87

The value of p^ is obtained below:

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371 450 -0.82

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Step 2

The test statistic is obtained as follows:

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Sample statistic Null Parameter SE p Po р. (1- р.) п 0.82- 0.87 0.87(1-0.87) 450 -0.05 0.016 =-3.13

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Step 3

Thus, the test statistic is –3.13.

p-value:

Step-by-step procedure to obtain the p-value using StatKey:

  • Choose Normal under Theoretical Distributions.
  • In Normal Distribution, click Edit Parameters.
  • Enter mean as 0 and standard deviation as 1 and click Ok.
  • Click Two Tail.
  • In Custom cutoff, enter the numerical cutoff value a...
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StatKey Theoretical Distribution Normal Distibution Reset Pt N Lt wo 0.40 0.35 0.30 0.25 0.20 q.998 0.00087 0.00087 0.15 0.10 0.05 0.00 4.0 3.0 2.0 1.0 0.0 1.0 2.0 4.C J.130 3.130

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