Answered: In a study conducted to investigate…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 4BGP

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Question

In a study conducted to investigate browsing activity by shoppers, each shopper was initially classified as a nonbrowser, light browser, or heavy browser. For each shopper, the study obtained a measure to determine how comfortable the shopper was in a store. Higher scores indicated greater comfort. Suppose the following data were collected.

Nonbrowser	Light Browser	Heavy Browser
4	5	4
5	5	7
6	5	5
3	4	7
3	7	4
4	4	6
5	6	5
3	5	7

(a)

Use ? = 0.05 to test for differences among comfort levels for the three types of browsers.

State the null and alternative hypotheses.

-H₀: Not all the population means are equal.
H_a: ?_NB = ?_LB = ?_HB

-H₀: ?_NB = ?_LB = ?_HB
H_a: ?_NB ≠ ?_LB ≠ ?_HB

-H₀: ?_NB = ?_LB = ?_HB
H_a: Not all the population means are equal.

-H₀: ?_NB ≠ ?_LB ≠ ?_HB
H_a: ?_NB = ?_LB = ?_HBH₀: At least two of the population means are equal.
H_a: At least two of the population means are different.

Find the value of the test statistic. (Round your answer to two decimal places.)

Statistic=??

Find the p-value. (Round your answer to three decimal places.)

p-value = ??

State your conclusion.

-Reject H₀. There is sufficient evidence to conclude that the mean comfort scores are not all the same for the three groups.

-Do not reject H₀. There is not sufficient evidence to conclude that the mean comfort scores are not all the same for the three groups.

- Do not reject H₀. There is sufficient evidence to conclude that the mean comfort scores are not all the same for the three groups.

-Reject H₀. There is not sufficient evidence to conclude that the mean comfort scores are not all the same for the three groups.

(b)

Use Fisher's LSD procedure to compare the comfort levels of nonbrowsers and light browsers. Use ? = 0.05.

Find the value of LSD. (Round your answer to two decimal places.)

LSD = ??

Find the absolute difference between sample means for the comfort levels of nonbrowsers and light browsers.

x_NB − x_LB = ??

What is your conclusion?

-There is a significant difference between the population means for the comfort levels of nonbrowsers and light browsers.

-There is not a significant difference between the population means for the comfort levels of nonbrowsers and light browsers.

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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