market research firm used a sample of individuals to rate the purchase potential of a particular product before and after the individuals saw a new television commercial about the product. The purchase potential ratings were based on a 0 to 10 scale, with higher values indicating a higher purchase potential. The null hypothesis stated that the mean rating "after" would be less than or equal to the mean rating "before." Rejection of this hypothesis would show that the commercial improved the mean purchase potential rating. Use ? = 0.05 and the following data to test the hypothesis and comment on the value of the commercial. Individual Purchase Rating After Before 1 6 5 2 6 5 3 7 8 4 4 3 5 3 6 6 9 8 7 7 5 8 6 6 State the null and alternative hypotheses. (Use ?d = mean rating after − mean rating before.) a) H0:?d ≤ 0 Ha:?d = 0 b) H0:?d ≤ 0 Ha:?d > 0 c) H0:?d ≠ 0 Ha:?d = 0 d) H0:?d = 0 Ha:?d ≠ 0 e) H0:?d > 0 Ha:?d ≤ 0 Calculate the value of the test statistic. (Round your answer to three decimal places.) answer: Calculate the p-value. (Round your answer to four decimal places.) p-value = _ State your conclusion. a) Do not reject H0. There is insufficient evidence to conclude that seeing the commercial improves the mean potential to purchase. b) Reject H0. There is insufficient evidence to conclude that seeing the commercial improves the mean potential to purchase. c) Do not Reject H0. There is sufficient evidence to conclude that seeing the commercial improves the mean potential to purchase. d) Reject H0. There is sufficient evidence to conclude that seeing the commercial improves the mean potential to purchase.

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.5: Correlation And Causation

Problem 11PPS

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Question

A market research firm used a sample of individuals to rate the purchase potential of a particular product before and after the individuals saw a new television commercial about the product. The purchase potential ratings were based on a 0 to 10 scale, with higher values indicating a higher purchase potential. The null hypothesis stated that the mean rating "after" would be less than or equal to the mean rating "before." Rejection of this hypothesis would show that the commercial improved the mean purchase potential rating. Use

? = 0.05

and the following data to test the hypothesis and comment on the value of the commercial.

Individual	Purchase Rating
After	Before
1	6	5
2	6	5
3	7	8
4	4	3
5	3	6
6	9	8
7	7	5
8	6	6

State the null and alternative hypotheses. (Use ?_d = mean rating after − mean rating before.)

a) H₀:?_d ≤ 0

H_a:?_d = 0

b) H₀:?_d ≤ 0

H_a:?_d > 0

c) H₀:?_d ≠ 0
H_a:?_d = 0

d) H₀:?_d = 0

H_a:?_d ≠ 0

e) H₀:?_d > 0

H_a:?_d ≤ 0

Calculate the value of the test statistic. (Round your answer to three decimal places.)

answer: ______

Calculate the p-value. (Round your answer to four decimal places.)

p-value = _______

State your conclusion.

a) Do not reject H₀. There is insufficient evidence to conclude that seeing the commercial improves the mean potential to purchase.

b) Reject H₀. There is insufficient evidence to conclude that seeing the commercial improves the mean potential to purchase.

c) Do not Reject H₀. There is sufficient evidence to conclude that seeing the commercial improves the mean potential to purchase.

d) Reject H₀. There is sufficient evidence to conclude that seeing the commercial improves the mean potential to purchase.

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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