Answered: Scores derived from a patient…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Scores derived from a patient satisfaction survey are Normally distributed with standard
deviation 7.5, with high scores indicating high satisfaction. You collect a sample of n = 36 from
a hospital in Reno and you find a sample mean of 48.8. You want to test if the mean score in
the Hospital is less than 50.
Question 1. What is the null hypothesis for this test?
A. H0:? ≠50.
B. H0:? =50.
C. H0:? ≠48.8.
D. H0:? =48.8.
Question 2. What is the one-sided alternative hypothesis for this test?
A. Ha:? ≠50.
B. Ha:? <50.
C. Ha:? >50.
Question 3. What is the z-statistic for the test?
A. -1.2
B. -0.96
C. -0.8
D. 0.01
Question 4. What is the p-value for the test?
A. 0.6745
B. 0.1151
C. 0.3371
D. 0.1685
Question 5. If we test at the 5% significance level (α = 0.05), what is your decision?
A. Reject the null hypothesis
B. Retain the null hypothesis
Question 6. What is your conclusion in the context of the problem.
A. The mean score in the hospital is less than 50
B. The mean score in the hospital is no different than 50
Question 7. Now you collect a sample of n = 36 from a hospital in Las Vegas and find a sample
mean of 46.5. You want to test if the mean score in the hospital in Las Vegas is less than 50.
What is the z-statistic for this new sample?
A. -13.5
B. -2.80
C. -1.25

Question 8. What is the p-value for the z-statistic you just found in Question 7?
A. 0.0026
B. 0.0052
C. 0.0123
D. 0.0230

Question 9. Can you reject the null hypothesis at the α = 0.05 (5% significance) level?
A. Yes
B. No

Question 10. What can you conclude?
A. The mean score in the hospital is less than 50
B.The mean score in the hospital is no different than 50

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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