3. Hypothesis tests about a population mean, population standard deviation unknown Airlines compute the weight of outbound flights using either standard average weights provided by the Federal Aviation Administration (FAA) or weights obtained from their own sample surveys. The FAA standard average weight for a passenger's carry-on items (personal items plus carry-on bags) is 16 pounds. Many airline companies have begun implementing fees for checked bags. Economic theory predicts that passengers will respond to the increase in the price of a checked bag by substituting carry-on bags for checked bags. As a result, the mean weight of a passenger's carry-on items is expected to increase after the implementation of the checked-bag fee. Suppose that a particular airline's passengers had a mean weight for their carry-on items of 16 pounds, the FAA standard average weight, before implementation of the checked-bag fee. The airline conducts a hypothesis test to determine whether the current mean weight of its passengers' carry-on items is more than 16 pounds. It selects a random sample of 67 passengers and weighs their carry-on items. The sample mean is x̄ x̄ = 17.1 pounds, and the sample standard deviation is s = 6.0 pounds. The airline uses a significance level of α = 0.05 to conduct its hypothesis test. The hypothesis test is ______ test. The test statistic follows a _______ distribution. The value of the test statistic is ______ . Use the Distributions tool to develop the critical value rejection rule. According to the critical value approach, the rejection rule is: Reject H₀ if t ≤ -1.668 Reject H₀ if t ≥ 1.668 Reject H₀ if t ≤ -1.997 or t ≥ 1.997 Reject H₀ if z ≥ 1.645 The p-value is . Using the critical value approach, the null hypothesis is _____ , because_____ . Using the p-value approach, the null hypothesis is ______ , because _____ . Therefore, you _____ conclude that the mean weight of the airline's passengers' carry-on items has increased after the implementation of the checked-bag fee.

3. Hypothesis tests about a population mean, population standard deviation unknown Airlines compute the weight of outbound flights using either standard average weights provided by the Federal Aviation Administration (FAA) or weights obtained from their own sample surveys. The FAA standard average weight for a passenger's carry-on items (personal items plus carry-on bags) is 16 pounds. Many airline companies have begun implementing fees for checked bags. Economic theory predicts that passengers will respond to the increase in the price of a checked bag by substituting carry-on bags for checked bags. As a result, the mean weight of a passenger's carry-on items is expected to increase after the implementation of the checked-bag fee. Suppose that a particular airline's passengers had a mean weight for their carry-on items of 16 pounds, the FAA standard average weight, before implementation of the checked-bag fee. The airline conducts a hypothesis test to determine whether the current mean weight of its passengers' carry-on items is more than 16 pounds. It selects a random sample of 67 passengers and weighs their carry-on items. The sample mean is x̄ x̄ = 17.1 pounds, and the sample standard deviation is s = 6.0 pounds. The airline uses a significance level of α = 0.05 to conduct its hypothesis test. The hypothesis test is __ test. The test statistic follows a _ distribution. The value of the test statistic is __ . Use the Distributions tool to develop the critical value rejection rule. According to the critical value approach, the rejection rule is: Reject H₀ if t ≤ -1.668 Reject H₀ if t ≥ 1.668 Reject H₀ if t ≤ -1.997 or t ≥ 1.997 Reject H₀ if z ≥ 1.645 The p-value is . Using the critical value approach, the null hypothesis is _ , because_ . Using the p-value approach, the null hypothesis is __ , because _ . Therefore, you ___ conclude that the mean weight of the airline's passengers' carry-on items has increased after the implementation of the checked-bag fee.

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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3. Hypothesis tests about a population mean, population standard deviation unknown

Airlines compute the weight of outbound flights using either standard average weights provided by the Federal Aviation Administration (FAA) or weights obtained from their own sample surveys. The FAA standard average weight for a passenger's carry-on items (personal items plus carry-on bags) is 16 pounds.

Many airline companies have begun implementing fees for checked bags. Economic theory predicts that passengers will respond to the increase in the price of a checked bag by substituting carry-on bags for checked bags. As a result, the mean weight of a passenger's carry-on items is expected to increase after the implementation of the checked-bag fee.

Suppose that a particular airline's passengers had a mean weight for their carry-on items of 16 pounds, the FAA standard average weight, before implementation of the checked-bag fee. The airline conducts a hypothesis test to determine whether the current mean weight of its passengers' carry-on items is more than 16 pounds. It selects a random sample of 67 passengers and weighs their carry-on items. The sample mean is x̄ x̄ = 17.1 pounds, and the sample standard deviation is s = 6.0 pounds. The airline uses a significance level of α = 0.05 to conduct its hypothesis test.

The hypothesis test is ______ test.

The test statistic follows a _______ distribution. The value of the test statistic is ______ .

Use the Distributions tool to develop the critical value rejection rule. According to the critical value approach, the rejection rule is:

Reject H₀ if t ≤ -1.668

Reject H₀ if t ≥ 1.668

Reject H₀ if t ≤ -1.997 or t ≥ 1.997

Reject H₀ if z ≥ 1.645

The p-value is .

Using the critical value approach, the null hypothesis is _____ , because_____ . Using the p-value approach, the null hypothesis is ______ , because _____ . Therefore, you _____ conclude that the mean weight of the airline's passengers' carry-on items has increased after the implementation of the checked-bag fee.

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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