The P&G marketing team has created two potential slogans for the new Smile toothpaste. The uplifting slogan is, “Smile when you buy Smile!”. The serious slogan is, “Buy Smile to keep your smile.” Before deciding which slogan to use, the marketing team runs an experiment to see how individuals respond to these two slogans. The marketing team recruits 46 people to participate in this experiment, randomly assigning 24 participants to read the uplifting slogan and 22 participants to read the serious slogan. After reading the slogans, all participants rate how likely they are to buy the new Smile toothpaste on a scale from 1 (definitely will NOT purchase) to 10 (definitely will purchase). The group of participants who read the uplifting slogan has a mean score of 6.67, with a sum of squares of 323. The group of participants who read the serious slogan has a mean score of 4.77, with a sum of squares of 221. Do participants who read the uplifting slogan versus the serious slogan differ significantly in how likely they are to purchase the new Smile toothpaste? Use a nondirectional alternative hypothesis and α = 0.10 to analyze this data. Answer all of the following questions. Please label each step with the appropriate letter. E. Compute and interpret Cohen’s d. F. Compute and interpret r2. G. Compute and interpret a 90% confidence interval.

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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The P&G marketing team has created two potential slogans for the new Smile toothpaste. The uplifting slogan is, “Smile when you buy Smile!”. The serious slogan is, “Buy Smile to keep your smile.” Before deciding which slogan to use, the marketing team runs an experiment to see how individuals respond to these two slogans. The marketing team recruits 46 people to participate in this experiment, randomly assigning 24 participants to read the uplifting slogan and 22 participants to read the serious slogan. After reading the slogans, all participants rate how likely they are to buy the new Smile toothpaste on a scale from 1 (definitely will NOT purchase) to 10 (definitely will purchase). The group of participants who read the uplifting slogan has a mean score of 6.67, with a sum of squares of 323. The group of participants who read the serious slogan has a mean score of 4.77, with a sum of squares of 221. Do participants who read the uplifting slogan versus the serious slogan differ significantly in how likely they are to purchase the new Smile toothpaste? Use a nondirectional alternative hypothesis and α = 0.10 to analyze this data. Answer all of the following questions. Please label each step with the appropriate letter.

E. Compute and interpret Cohen’s d.

F. Compute and interpret r2.

G. Compute and interpret a 90% confidence interval.

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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