Answered: b) Calculate the value of the test…

Name: A hotel chain wants to determine whether there is a difference in the
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Description: A hotel chain wants to determine whether there is a difference in the length of stays at two of its different brands of hotels. A simple random sample of 100 stay lengths was taken for each hotel brand. These data are shown below. Assume that the var

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 hotel chain wants to determine whether there is a difference in the length of stays at two of its different brands of hotels. A simple random sample of 100 stay lengths was taken for each hotel brand. These data are shown below. Assume that the variances are not equal.

a) State the appropriate null and alternative hypotheses.

b) Based on these sample data and a 0.01 level of significance, what conclusion should be made about the average length of stay at these two hotel chains?

Click the icon for sample data on the length of stays at these hotel chains.

a) State the appropriate null and alternative hypotheses. Let μ1 be the population mean length of stay at hotel brand 1, and let μ2 be the population mean length of stay at hotel brand 2.

A. H0: μ1−μ2=0

HA: μ1−μ2≠0

Your answer is correct.

b) Calculate the value of the test statistic.

The test statistic is

(Round to two decimal places as needed.)

(The space separates the column values) Hotel_Brand_1_Stay_Length Hotel_Brand_2_Stay_Length

4 6
1 2
3 1
1 3
1 12
4 3
7 7
1 3
6 3
2 4
5 1
1 7
2 4
1 3
3 3
4 2
2 6
4 4
2 5
9 1
5 2
1 1
4 3
2 2
3 2
9 3
2 1
4 3
5 2
5 11
1 5
7 5
2 7
2 6
9 9
6 4
1 1
9 1
3 5
5 13
6 1
4 10
3 1
5 1
2 3
4 1
2 8
2 8
3 2
2 3
1 3
6 1
6 2
5 6
2 2
2 2
2 3
2 2
2 8
3 3
1 8
2 3
1 2
1 1
2 5
2 4
2 3
3 2
3 3
2 8
4 2
3 2
5 5
3 2
2 3
1 3
4 1
3 6
1 4
3 3
5 3
3 5
4 4
4 4
3 4
3 1
5 5
1 3
2 8
3 3
3 4
4 4
6 2
8 4
3 2
2 6
3 2
3 4
7 6
3 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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