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Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

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BuyFindarrow_forward

Essentials of Statistics for the B...

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.

  1. 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.
  2. b. Calculate r2 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 α=0.05 for the given question

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 H0:μ1μ2=0 and Alternate Hypothesis is H1:μ1μ20

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

df=n1+n22=100+1002=198

For a two-tailed test with α=0.05 and df=198 , the critical value (CV)  is obtained from the t-table as t=±1.960

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

t=(M1M2)(μ1μ2)sM1M2

But before that calculate pooled variance, sp2 , using formula:

sp2=(df1)s12+(df2)s22df1+df2

Substitute 85 for s1 , 91 for s2 and 99 for both df1 and df2 in the above formula

sp2=(99)852+(99)91299+99=99(852+912)2(99

b.

To determine

To Find: The value of r2 to measure effect size for the mean difference

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