A study is made of residents in Phoenix and its suburbs concerning the proportion of residents who subscribe to Sporting News. A random sample of n1 = 86 urban residents showed that r1 = 13 subscribed, and a random sample of n2 = 95 suburban residents showed that r2 = 20 subscribed. Does this indicate that a higher proportion of suburban residents subscribe to Sporting News? Use a 5% level of significance. What are we testing in this problem? single meandifference of proportions single proportiondifference of meanspaired difference
A study is made of residents in Phoenix and its suburbs concerning the proportion of residents who subscribe to Sporting News. A random sample of n1 = 86 urban residents showed that r1 = 13 subscribed, and a random sample of n2 = 95 suburban residents showed that r2 = 20 subscribed. Does this indicate that a higher proportion of suburban residents subscribe to Sporting News? Use a 5% level of significance. What are we testing in this problem? single meandifference of proportions single proportiondifference of meanspaired difference
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
A study is made of residents in Phoenix and its suburbs concerning the proportion of residents who subscribe to Sporting News. A random sample of
n1 = 86
urban residents showed that
r1 = 13
subscribed, and a random sample of
n2 = 95
suburban residents showed that
r2 = 20
subscribed. Does this indicate that a higher proportion of suburban residents subscribe to Sporting News? Use a 5% level of significance.
What are we testing in this problem?
single meandifference of proportions single proportiondifference of meanspaired difference
(a) What is the level of significance?
State the null and alternate hypotheses.
(b) What sampling distribution will you use? What assumptions are you making?
What is the value of the sample test statistic? (Test the difference p1 − p2. Do not use rounded values. Round your final answer to two decimal places.)
(c) Find (or estimate) the P-value.
Sketch the sampling distribution and show the area corresponding to the P-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??
(e) Interpret your conclusion in the context of the application.
State the null and alternate hypotheses.
H0: p1 < p2; H1: p1 = p2H0: p1 = p2; H1: p1 > p2 H0: p1 = p2; H1: p1 < p2H0: p1 = p2; H1: p1 ≠ p2
(b) What sampling distribution will you use? What assumptions are you making?
The Student's t. We assume the population distributions are approximately normal.The standard normal. The number of trials is sufficiently large. The Student's t. The number of trials is sufficiently large.The standard normal. We assume the population distributions are approximately normal.
What is the value of the sample test statistic? (Test the difference p1 − p2. Do not use rounded values. Round your final answer to two decimal places.)
(c) Find (or estimate) the P-value.
P-value > 0.2500.125 < P-value < 0.250 0.050 < P-value < 0.1250.025 < P-value < 0.0500.005 < P-value < 0.025P-value < 0.005
Sketch the sampling distribution and show the area corresponding to the P-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??
At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) Interpret your conclusion in the context of the application.
There is sufficient evidence at the 0.05 level to conclude that the proportion of suburban residents subscribing to Sporting News is higher.There is insufficient evidence at the 0.05 level to conclude that the proportion of suburban residents subscribing to Sporting News is higher.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 2 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman