Question

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:

*H*0:*p* = 0.87

*Ha*:*p* ≠ 0.87

Find the p-value for this hypothesis test for a proportion and round your answer to 3 decimal places.

The following table can be utilized which provides areas under the Standard Normal Curve:

z | 0.00 | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 |

-2.9 | 0.002 | 0.002 | 0.002 | 0.002 | 0.002 | 0.002 | 0.002 | 0.001 | 0.001 | 0.001 |

-2.8 | 0.003 | 0.002 | 0.002 | 0.002 | 0.002 | 0.002 | 0.002 | 0.002 | 0.002 | 0.002 |

-2.7 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 |

-2.6 | 0.005 | 0.005 | 0.004 | 0.004 | 0.004 | 0.004 | 0.004 | 0.004 | 0.004 | 0.004 |

-2.5 | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 | 0.005 | 0.005 | 0.005 | 0.005 | 0.005 |

Step 1

The provided information are:

Sample size (*n*) = 450

Hypothesised proportion (*p*_{o})=0.87

From the provided setup it is known that the test is two sided.

Step 2

The test statistic can b...

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