# 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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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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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:

Step 2

The test statistic is obtained as follows:

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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