A random sample of 36 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 15 and the sample standard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is 14.5.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question

A random sample of 36 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 15 and the sample standard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is 14.5.

(a) Is it appropriate to use a Student's t distribution? Explain.
O Yes, because the x distribution is mound-shaped and symmetric and is unknown.
O No, the x distribution is skewed left.
O No, the x distribution is skewed right.
O No, the x distribution is not symmetric.
O No, a is known.
How many degrees of freedom do we use?
(b) What are the hypotheses?
O Ho: = 14.5; H₁: μ< 14.5
O Ho: H= 14.5; H₁: μ# 14.5
O Ho:
14.5; H₁: μ = 14.5
O Ho: M = 14.5; H₁: μ> 14.5
O Ho: > 14.5; H₁: μ = 14.5
(c) Compute the t value of the sample test statistic. (Round your answer to three decimal places.)
t =
(d) Estimate the P-value for the test.
OP-value > 0.250
O 0.100 < P-value < 0.250
O 0.050 < P-value < 0.100
O 0.010 < P-value < 0.050
O P-value < 0.010
(e) Do we reject or fail to reject Ho?
O At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
O At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
O At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(f) Interpret the results.
O There is sufficient evidence at the 0.05 level to reject the null hypothesis.
O There is insufficient evidence at the 0.05 level to reject the null hypothesis.
Transcribed Image Text:(a) Is it appropriate to use a Student's t distribution? Explain. O Yes, because the x distribution is mound-shaped and symmetric and is unknown. O No, the x distribution is skewed left. O No, the x distribution is skewed right. O No, the x distribution is not symmetric. O No, a is known. How many degrees of freedom do we use? (b) What are the hypotheses? O Ho: = 14.5; H₁: μ< 14.5 O Ho: H= 14.5; H₁: μ# 14.5 O Ho: 14.5; H₁: μ = 14.5 O Ho: M = 14.5; H₁: μ> 14.5 O Ho: > 14.5; H₁: μ = 14.5 (c) Compute the t value of the sample test statistic. (Round your answer to three decimal places.) t = (d) Estimate the P-value for the test. OP-value > 0.250 O 0.100 < P-value < 0.250 O 0.050 < P-value < 0.100 O 0.010 < P-value < 0.050 O P-value < 0.010 (e) Do we reject or fail to reject Ho? O At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. O At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. O At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (f) Interpret the results. O There is sufficient evidence at the 0.05 level to reject the null hypothesis. O There is insufficient evidence at the 0.05 level to reject the null hypothesis.
Expert Solution
steps

Step by step

Solved in 4 steps

Blurred answer
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
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 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…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
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
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman