menu
bartleby
search
close search
Hit Return to see all results

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 ≠ 0.87Find 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:z0.000.010.020.030.040.050.060.070.080.09-2.90.0020.0020.0020.0020.0020.0020.0020.0010.0010.001-2.80.0030.0020.0020.0020.0020.0020.0020.0020.0020.002-2.70.0030.0030.0030.0030.0030.0030.0030.0030.0030.003-2.60.0050.0050.0040.0040.0040.0040.0040.0040.0040.004-2.50.0060.0060.0060.0060.0060.0050.0050.0050.0050.005

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:

H0: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
check_circleAnswer
Step 1

The provided information are:

Sample size (n) = 450

Hypothesised proportion (po)=0.87

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

371
-=0.824
450
Sample proportion of successful knee surgeries (p)
So, the P-value for the two tailed test can be found using the formula
P-value 2P(Z>)
stor
help_outline

Image Transcriptionclose

371 -=0.824 450 Sample proportion of successful knee surgeries (p) So, the P-value for the two tailed test can be found using the formula P-value 2P(Z>) stor

fullscreen
Step 2

The test statistic can b...

р-р,.
stt
Р.(1-р.)
п
0.824 0.87
0.87x (1-0.87)
450
-2.90
help_outline

Image Transcriptionclose

р-р,. stt Р.(1-р.) п 0.824 0.87 0.87x (1-0.87) 450 -2.90

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Our solutions are written by experts, many with advanced degrees, and available 24/7

See Solution
Tagged in

Math

Statistics

Hypothesis Testing

Related Statistics Q&A

Find answers to questions asked by student like you

Show more Q&A add
question_answer

Q: Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took th...

A: Given data of glucose reading for 8 weeks92 87 82 107 99 109 85 89The sample x-bar is 93.8 . x is no...

question_answer

Q: what is the class boundaries 16.5, 20.5, 24.5, 28.5, 32.5, 36.5, and 40.5.

A: Class boundaries are those numbers which are used to separate the classes.It is the midpoint of the ...

question_answer

Q: How would I construct a stem and leaf plot using these numbers 57 54 52 55 51 56 61 68 56 55 54 61 5...

A: Introduction:The numbers here are all two-digit numbers. So, you can consider the digit in the ten’s...

question_answer

Q: Select the statistic test that best fits each description. Number of heart attacks per blood type (a...

A: Introduction:A brief introduction to the various tests suggested here is given below:T-test independ...

question_answer

Q: A researcher wants to investigate whether mindfulness training improves ability for employees to not...

A: A dependent variable is a variable which is being tested and measured in any scientific experiment. 

question_answer

Q: A test consists of 940 true or false questions. If the student guesses on each​ question, what is th...

A: Given number of true or false questions = n = 940.Probability of correct answer p = 1/2Here we can s...

question_answer

Q: See attachment.

A: Given X(n,p) is a binomial random variable with parameters n,p.n is total number of trailsp is proba...

question_answer

Q: Use the normal approximation to the binominal to approximate the probabilities. A gardener buys a pa...

A: Normal approximation to the binomial:If a random variable X ~ B(n, p) in which n is large and p is c...

question_answer

Q: You are asked to design a study to investigate the effectiveness of the Atkins diet (IV = diet, DV =...

A: Consider the population of all individuals in a particular city. A random sample of 40 individuals i...

Sorry about that. What wasn’t helpful?