Question

In: Statistics and Probability

With increases in obesity rates over the past several decades, health care providers have become concerned...

With increases in obesity rates over the past several decades, health care providers have become concerned about the effects of obesity on health. As a health psychologist, you are interested in people’s perceptions and responses to food as this might influence obesity. You are curious if people that are impulsive or have difficult with impulse control are more likely to be obese and if they perceive sweet, high calorie foods as being more desirable than the general population. Given this, you screen a group of participants and recruit participants (n=20) that have high impulsivity scores (that is, they are more impulsive). From your sample, you collect participant’s weight and scores on the Food Perception Inventory (FPI) which measures individual’s preference for high calorie foods. For obesity, you know the national mean (168) and standard deviation (26.38), but you only know the population mean (103) for the FPI. Using the data below, answer the following questions:

Participant ID

Weight

FPI

1

204

115

2

198

111

3

219

119

4

250

122

5

170

105

6

232

110

7

178

104

8

177

107

9

192

109

10

198

110

11

203

115

12

211

114

13

198

112

14

212

120

15

215

119

16

236

120

17

196

115

18

198

115

19

180

112

20

210

121

Questions:

1. Calculate a one sample test for Weight and report the result

2. What is your decision for Weight (how will you determine if this sample is unique or rare)? Interpret your result

3. Calculate a one sample test for FPI and report the result

4. What is your decision for FPI? Interpret your result

Solutions

Expert Solution

1. The results are:

168.000 hypothesized value
203.850 mean Weight
20.402 std. dev.
4.562 std. error
20 n
19 df
7.858 t
2.18E-07 p-value (two-tailed)

2. The p-value is 0.0000.

Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that µ ≠ 168.

3. The results are:

103.000 hypothesized value
113.750 mean FPI
5.340 std. dev.
1.194 std. error
20 n
19 df
9.003 t
2.78E-08 p-value (two-tailed)

4. The p-value is 0.0000.

Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that µ ≠ 103.


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