Chapter 10, Problem 17P

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8th Edition

Frederick J Gravetter + 1 other

ISBN: 9781133956570

Textbook Problem

Does posting caloric content for menu items affect people’s choices in fast-food restaurants? According to results obtained by Elbel, Gyamfi, and Kersh (2011), the answer is no. The researchers monitored the calorie content of food purchases for children and adolescents in four large fast-food chains before and after mandatory labeling began in New York City. Although most of the adolescents reported noticing the calorie labels, apparently the labels had no effect on their choices. Data similar to the. results obtained show an average of M = 786 calories per meal with s = 85 for n = 100 children and adolescents before the labeling, compared to an average of M = 772 calories with s = 91 for a similar sample of n = 100 after the mandatory posting.

- a. Use a Iwo-tailed test with α =.05 to determine whether the mean number of calories after the posting is significantly different than before calorie content was posted.
- b. Calculate
*r*^{2}to measure effect size for the mean difference.

**a.**

To determine

**To check:** Whether the mean number of calories after the posting is significantly different than before calorie content was posted using two-tailed test at

Explanation

**Given info:**

Two samples each with size 100 have means 786 and 772 respectively. Similarly, both of them have standard deviations equal to 85 and 91 respectively.

**Calculations:**

Step 1: Null Hypothesis is

Step 2: For the given sample, the t-statistics will have degrees of freedom equals:

For a two-tailed test with
*t*-table as

Step 3: The *t*-statistics is calculated using formula:

But before that calculate pooled variance,

Substitute 85 for

**b.**

To determine

**To Find:** The value of

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