USA TODAY (October 14, 2016) reported that Americans spend 4.1 hours per weekday checking work email. This was an estimate based on a survey of 1,004 white-collar workers in the United States. (a) Suppose that you would like to know if there is evidence that the mean time spent checking work email for white-collar workers in the United States is more than half of the 8-hourwork day. What would you need to assume about the sample in order to use the given sample data to answer this question? (Select all that apply.) We would need to assume that all white-collar workers were surveyed or the sample is representative of the population of white-collar workers in the United States.We would need to assume that all observations are dependent or all observations are independent.We would need to assume that the distribution of the population of times is normal or that the sample size is small.We would need to assume that the sample was randomly selected or is representative of the population of white-collar workers in the United States.We would need to assume that the distribution of the population of times is normal or that the sample size is large. (b) Given that any concerns about the sample were satisfactorily addressed, carry out a test to decide if there is evidence that the mean time spent checking work email for white-collar workers in the United States is more than half of the 8-hour work day. Suppose that the sample standard deviation was s = 1.2 hours. Use a 0.05 significance level. State the appropriate null and alternative hypotheses. H0: μ = 4 Ha: μ < 4 H0: μ > 4 Ha: μ < 4 H0: μ = 4 Ha: μ ≠ 4 H0: μ = 4 Ha: μ > 4 H0: μ < 4 Ha: μ > 4 Find the test statistic and P-value. (Use a table or technology. Round your test statistic to one decimal place and your P-value to three decimal places.) t= P-value = State the conclusion in the problem context. We fail to reject H0. We do not have convincing evidence that the mean time spent checking work email for white-collar workers in the U.S. is more than half of the 8-hour work day.We reject H0. We do not have convincing evidence that the mean time spent checking work email for white-collar workers in the U.S. is more than half of the 8-hour work day. We reject H0. We have convincing evidence that the mean time spent checking work email for white-collar workers in the U.S. is more than half of the 8-hour work day.We fail to reject H0. We have convincing evidence that the mean time spent checking work email for white-collar workers in the U.S. is more than half of the 8-hour work day

USA TODAY (October 14, 2016) reported that Americans spend 4.1 hours per weekday checking work email. This was an estimate based on a survey of 1,004 white-collar workers in the United States. (a) Suppose that you would like to know if there is evidence that the mean time spent checking work email for white-collar workers in the United States is more than half of the 8-hourwork day. What would you need to assume about the sample in order to use the given sample data to answer this question? (Select all that apply.) We would need to assume that all white-collar workers were surveyed or the sample is representative of the population of white-collar workers in the United States.We would need to assume that all observations are dependent or all observations are independent.We would need to assume that the distribution of the population of times is normal or that the sample size is small.We would need to assume that the sample was randomly selected or is representative of the population of white-collar workers in the United States.We would need to assume that the distribution of the population of times is normal or that the sample size is large. (b) Given that any concerns about the sample were satisfactorily addressed, carry out a test to decide if there is evidence that the mean time spent checking work email for white-collar workers in the United States is more than half of the 8-hour work day. Suppose that the sample standard deviation was s = 1.2 hours. Use a 0.05 significance level. State the appropriate null and alternative hypotheses. H0: μ = 4 Ha: μ < 4 H0: μ > 4 Ha: μ < 4 H0: μ = 4 Ha: μ ≠ 4 H0: μ = 4 Ha: μ > 4 H0: μ < 4 Ha: μ > 4 Find the test statistic and P-value. (Use a table or technology. Round your test statistic to one decimal place and your P-value to three decimal places.) t= P-value = State the conclusion in the problem context. We fail to reject H0. We do not have convincing evidence that the mean time spent checking work email for white-collar workers in the U.S. is more than half of the 8-hour work day.We reject H0. We do not have convincing evidence that the mean time spent checking work email for white-collar workers in the U.S. is more than half of the 8-hour work day. We reject H0. We have convincing evidence that the mean time spent checking work email for white-collar workers in the U.S. is more than half of the 8-hour work day.We fail to reject H0. We have convincing evidence that the mean time spent checking work email for white-collar workers in the U.S. is more than half of the 8-hour work day

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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USA TODAY (October 14, 2016) reported that Americans spend 4.1 hours per weekday checking work email. This was an estimate based on a survey of 1,004 white-collar workers in the United States.

(a)

Suppose that you would like to know if there is evidence that the mean time spent checking work email for white-collar workers in the United States is more than half of the 8-hourwork day. What would you need to assume about the sample in order to use the given sample data to answer this question? (Select all that apply.)

We would need to assume that all white-collar workers were surveyed or the sample is representative of the population of white-collar workers in the United States.We would need to assume that all observations are dependent or all observations are independent.We would need to assume that the distribution of the population of times is normal or that the sample size is small.We would need to assume that the sample was randomly selected or is representative of the population of white-collar workers in the United States.We would need to assume that the distribution of the population of times is normal or that the sample size is large.

(b)

Given that any concerns about the sample were satisfactorily addressed, carry out a test to decide if there is evidence that the mean time spent checking work email for white-collar workers in the United States is more than half of the 8-hour work day. Suppose that the sample standard deviation was

s = 1.2 hours.

Use a 0.05 significance level.

State the appropriate null and alternative hypotheses.

H₀: μ = 4

H_a: μ < 4

H₀: μ > 4

H_a: μ < 4

H₀: μ = 4

H_a: μ ≠ 4

H₀: μ = 4

H_a: μ > 4

H₀: μ < 4

H_a: μ > 4

Find the test statistic and P-value. (Use a table or technology. Round your test statistic to one decimal place and your P-value to three decimal places.)

t= P-value =

State the conclusion in the problem context.

We fail to reject H₀. We do not have convincing evidence that the mean time spent checking work email for white-collar workers in the U.S. is more than half of the 8-hour work day.We reject H₀. We do not have convincing evidence that the mean time spent checking work email for white-collar workers in the U.S. is more than half of the 8-hour work day. We reject H₀. We have convincing evidence that the mean time spent checking work email for white-collar workers in the U.S. is more than half of the 8-hour work day.We fail to reject H₀. We have convincing evidence that the mean time spent checking work email for white-collar workers in the U.S. is more than half of the 8-hour work day.

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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