A random sample of 36 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 13 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 12.5. In USE SALT (a) Is it appropriate to use a Student's t distribution? Explain. O Yes, because the x distribution is mound-shaped and symmetric and o 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, o is known. How many degrees of freedom do we use? (b) What are the hypotheses? O Ho: H = 12.5; H,: µ # 12.5 О но: и 3 12.5;B н,: и> 12.5 О но: и> 12.5;B н,: и 3 12.5 О но: и 3 12.5;B н,: и < 12.5 О но: и < 12.5;B н,: и— 12.5 (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. O P-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 H,? O At the a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. O At the a = 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 a = 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.
A random sample of 36 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 13 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 12.5. In USE SALT (a) Is it appropriate to use a Student's t distribution? Explain. O Yes, because the x distribution is mound-shaped and symmetric and o 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, o is known. How many degrees of freedom do we use? (b) What are the hypotheses? O Ho: H = 12.5; H,: µ # 12.5 О но: и 3 12.5;B н,: и> 12.5 О но: и> 12.5;B н,: и 3 12.5 О но: и 3 12.5;B н,: и < 12.5 О но: и < 12.5;B н,: и— 12.5 (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. O P-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 H,? O At the a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. O At the a = 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 a = 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.
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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Transcribed Image Text:A random sample of 36 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 13 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 12.5.
In USE SALT
(a) Is it appropriate to use a Student's t distribution? Explain.
O Yes, because the x distribution is mound-shaped and symmetric and o 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, o is known.
How many degrees of freedom do we use?
(b) What are the hypotheses?
О Но: и 3D 12.5; Н,: и # 12.5
о но: и 3 12.5; H: и > 12.5
О Но: и> 12.5; Н,: и %3D 12.5
О Но: и 3 12.5; H,: и < 12.5
Но: и < 12.5; H: и 3D 12.5
(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.
O P-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 H?
O At the a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
At the a = 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 a = 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.
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