A set of solar batteries is used in a research satellite. The satellite can run on only one battery, but it runs best if more than one battery is used. The variance o2 of lifetimes of these batteries affects the useful lifetime of the satellite before it goes dead. If the variance is too small, all the batteries will tend to die at once. Why? If the variand too large, the batteries are simply not dependable. Why? Engineers have determined that a variance of a223 months (squared) is most desirable for these batteries. A random sample of 24 batteries gave a sample variance of 15.8 months (squared). Using a 0.05 level of significance, test the claim that d2 23 against the claim that 2 different from 23. (a) What is the level of significance? State the null and alternate hypotheses Hoi ²231 H₂0² < 23 OH ²231 M₁ 0² 23 Hol 0²231 M₂1 0²-23 OH ²231 H₂ ²23 (b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.) What are the degrees of freedom? pom 7 What assumptions are you making about the original distribution? O We assume a normal population distribution. O We assume a uniform population distribution. We assume a binomial population distribution. O We assume a exponential population distribution. (c) Find or estimate the P-value of the sample test statistic. O Pivalue> 0.100 O 0.050 P-value 0.100 O 0.025 < P-value < 0.050 O 0.010 P-value < 0.025 O 0.005 P-value < 0.010 OP-value < 0.005 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Since the P-value> a, we fail to reject the null hypothesis. O Since the P-value> a, we reject the null hypothesis. O Since the P-value sa, we reject the null hypothesis. O Since the P-value s a, we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. O At the 5% level of significance, there is insufficient evidence to conclude that the variance of battery life is different from 23. O At the 5% level of significance, there is sufficient evidence to conclude that the variance of battery life is different from 23.
A set of solar batteries is used in a research satellite. The satellite can run on only one battery, but it runs best if more than one battery is used. The variance o2 of lifetimes of these batteries affects the useful lifetime of the satellite before it goes dead. If the variance is too small, all the batteries will tend to die at once. Why? If the variand too large, the batteries are simply not dependable. Why? Engineers have determined that a variance of a223 months (squared) is most desirable for these batteries. A random sample of 24 batteries gave a sample variance of 15.8 months (squared). Using a 0.05 level of significance, test the claim that d2 23 against the claim that 2 different from 23. (a) What is the level of significance? State the null and alternate hypotheses Hoi ²231 H₂0² < 23 OH ²231 M₁ 0² 23 Hol 0²231 M₂1 0²-23 OH ²231 H₂ ²23 (b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.) What are the degrees of freedom? pom 7 What assumptions are you making about the original distribution? O We assume a normal population distribution. O We assume a uniform population distribution. We assume a binomial population distribution. O We assume a exponential population distribution. (c) Find or estimate the P-value of the sample test statistic. O Pivalue> 0.100 O 0.050 P-value 0.100 O 0.025 < P-value < 0.050 O 0.010 P-value < 0.025 O 0.005 P-value < 0.010 OP-value < 0.005 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Since the P-value> a, we fail to reject the null hypothesis. O Since the P-value> a, we reject the null hypothesis. O Since the P-value sa, we reject the null hypothesis. O Since the P-value s a, we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. O At the 5% level of significance, there is insufficient evidence to conclude that the variance of battery life is different from 23. O At the 5% level of significance, there is sufficient evidence to conclude that the variance of battery life is different from 23.
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
100%
Transcribed Image Text:A set of solar batteries is used in a research satellite. The satellite can run on only one battery, but it runs best if more than one battery is used. The variance 2 of lifetimes of these batteries affects the useful lifetime of the satellite before it goes dead. If the variance is too small, all the batteries will tend to die at once. Why? If the variance is
too large, the batteries are simply not dependable. Why? Engineers have determined that a variance of o2 = 23 months (squared) is most desirable for these batteries. A random sample of 24 batteries gave sample variance of 15.8 months (squared). Using a 0.05 level of significance, test the claim that o2 = 23 against the claim that o² is
different from 23.
(a) What is the level of significance?
State the null and alternate hypotheses.
O Ho: 0² = 23; H₁:0² < 23
O
o Hoi a = 23; Hội gả, 23
O Ho: 0² > 23: H₁: 0² = 23
O Ho: 0²= 23: H₁: 0² #23
(b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)
What are the degrees
freedom?
What assumptions are you making about the original distribution?
O We assume a normal population distribution.
O We assume a uniform population distribution.
O We assume a binomial population distribution.
O We assume a exponential population distribution.
(c) Find or estimate the P-value of the sample test statistic.
O P-value > 0.100
O 0.050 < P-value < 0.100
O 0.025 < P-value < 0.050
O 0.010 < P-value < 0.025
O 0.005 < P-value < 0.010
O P-value < 0.005
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?
O Since the P-value > a, we fail to reject the null hypothesis.
O Since the P-value > a, we reject the null hypothesis.
O Since the P-value ≤ a, we reject the null hypothesis.
O Since the P-value ≤ a, we fail to reject the null hypothesis.
(e) Interpret your conclusion in the context of the application.
O At the 5% level of significance, there is insufficient evidence to conclude that the variance of battery life is different from 23.
O At the 5% level of significance, there is sufficient evidence to conclude that the variance of battery life is different from 23.
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 2 steps
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