In a study of computer use, 1000 randomly selected Canadian Internet users were asked how much time they spend using the Internet in a typical week. The mean of the sample observations was 12.8 hours. (a) The sample standard deviation was not reported, but suppose that it was 6 hours. Carry out a hypothesis test with a significance level of 0.05 to decide if there is convincing evidence that the mean time spent using the Internet by Canadians is greater than 12.6 hours. (Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to four decimal places.) t=P-value= State the conclusion in the problem context. Reject H0. We have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.6 hours.Do not reject H0. We have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.6 hours. Reject H0. We do not have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.6 hours.Do not reject H0. We do not have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.6 hours. (b) Now suppose that the sample standard deviation was 3 hours. Carry out a hypothesis test with a significance level of 0.05 to decide if there is convincing evidence that the mean time spent using the Internet by Canadians is greater than 12.6 hours. (Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to four decimal places.) t=P-value= State the conclusion in the problem context. Do not reject H0. We have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.6 hours.Do not reject H0. We do not have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.6 hours. Reject H0. We have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.6 hours.Reject H0. We do not have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.6 hours. (c) Explain why the hypothesis tests resulted in different conclusions for part (a) and part (b). The larger standard deviation means that you can expect more variability in measurements and greater deviations from the mean. This explains why H0 is rejected when the sample standard deviation is 3, but not when the sample standard deviation is 6.The larger standard deviation means that you can expect less variability in measurements and smaller deviations from the mean. This explains why H0 is rejected when the sample standard deviation is 6, but not when the sample standard deviation is 3. The smaller standard deviation means that you can expect more variability in measurements and greater deviations from the mean. This explains why H0 is rejected when the sample standard deviation is 3, but not when the sample standard deviation is 6.The smaller standard deviation means that you can expect less variability in measurements and smaller deviations from the mean. This explains why H0 is rejected when the sample standard deviation is 6, but not when the sample

In a study of computer use, 1000 randomly selected Canadian Internet users were asked how much time they spend using the Internet in a typical week. The mean of the sample observations was 12.8 hours. (a) The sample standard deviation was not reported, but suppose that it was 6 hours. Carry out a hypothesis test with a significance level of 0.05 to decide if there is convincing evidence that the mean time spent using the Internet by Canadians is greater than 12.6 hours. (Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to four decimal places.) t=P-value= State the conclusion in the problem context. Reject H0. We have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.6 hours.Do not reject H0. We have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.6 hours. Reject H0. We do not have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.6 hours.Do not reject H0. We do not have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.6 hours. (b) Now suppose that the sample standard deviation was 3 hours. Carry out a hypothesis test with a significance level of 0.05 to decide if there is convincing evidence that the mean time spent using the Internet by Canadians is greater than 12.6 hours. (Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to four decimal places.) t=P-value= State the conclusion in the problem context. Do not reject H0. We have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.6 hours.Do not reject H0. We do not have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.6 hours. Reject H0. We have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.6 hours.Reject H0. We do not have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.6 hours. (c) Explain why the hypothesis tests resulted in different conclusions for part (a) and part (b). The larger standard deviation means that you can expect more variability in measurements and greater deviations from the mean. This explains why H0 is rejected when the sample standard deviation is 3, but not when the sample standard deviation is 6.The larger standard deviation means that you can expect less variability in measurements and smaller deviations from the mean. This explains why H0 is rejected when the sample standard deviation is 6, but not when the sample standard deviation is 3. The smaller standard deviation means that you can expect more variability in measurements and greater deviations from the mean. This explains why H0 is rejected when the sample standard deviation is 3, but not when the sample standard deviation is 6.The smaller standard deviation means that you can expect less variability in measurements and smaller deviations from the mean. This explains why H0 is rejected when the sample standard deviation is 6, but not when the sample

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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(a)

The sample standard deviation was not reported, but suppose that it was 6 hours. Carry out a hypothesis test with a significance level of 0.05 to decide if there is convincing evidence that the mean time spent using the Internet by Canadians is greater than 12.6 hours. (Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to four decimal places.)

t=P-value=

State the conclusion in the problem context.

Reject H₀. We have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.6 hours.Do not reject H₀. We have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.6 hours. Reject H₀. We do not have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.6 hours.Do not reject H₀. We do not have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.6 hours.

(b)

Now suppose that the sample standard deviation was 3 hours. Carry out a hypothesis test with a significance level of 0.05 to decide if there is convincing evidence that the mean time spent using the Internet by Canadians is greater than 12.6 hours. (Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to four decimal places.)

t=P-value=

State the conclusion in the problem context.

Do not reject H₀. We have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.6 hours.Do not reject H₀. We do not have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.6 hours. Reject H₀. We have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.6 hours.Reject H₀. We do not have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.6 hours.

(c)

Explain why the hypothesis tests resulted in different conclusions for part (a) and part (b).

The larger standard deviation means that you can expect more variability in measurements and greater deviations from the mean. This explains why H₀ is rejected when the sample standard deviation is 3, but not when the sample standard deviation is 6.The larger standard deviation means that you can expect less variability in measurements and smaller deviations from the mean. This explains why H₀ is rejected when the sample standard deviation is 6, but not when the sample standard deviation is 3. The smaller standard deviation means that you can expect more variability in measurements and greater deviations from the mean. This explains why H₀ is rejected when the sample standard deviation is 3, but not when the sample standard deviation is 6.The smaller standard deviation means that you can expect less variability in measurements and smaller deviations from the mean. This explains why H₀ is rejected when the sample standard deviation is 6, but not when the sample standard deviation is 3.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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