Question
Individuals have their HEI measured on two different days with the first and second day indicated by the variable daycode. A number of researchers argue that individuals will have a higher-quality diet for the second interview because they will adjust their diet after the first interview. You are asked to perform an appropriate hypothesis test to determine if there is strong evidence to conclude that individuals have a higher $\mathrm{HEI}$ on the second day compared to the first day.
Step 1
e., \( \mu_D = 0 \) where \( \mu_D \) is the mean difference in HEI scores (second day HEI minus first day HEI). - Alternative Hypothesis (\(H_a\)): The HEI scores are higher on the second day, i.e., \( \mu_D > 0 \). Show more…
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A nutritionist claims that individuals tend to report decreasing dietary intake the more they are interviewed. To investigate this claim, a random sample of eight female university students was asked to record their dietary intake for two consecutive days. An analysis on their total dietary intake (in kcal) gave the following results: Student | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 --- | --- | --- | --- | --- | --- | --- | --- | --- Day 1 | 1905 | 2237 | 1863 | 2291 | 2211 | 1428 | 1062 | 1705 Day 2 | 1658 | 1479 | 1100 | 2116 | 1999 | 1097 | 1283 | 2424 Assume that the differences in total dietary intake are normally distributed. Using a 5% level of significance, test the claim that a higher dietary intake is observed on day 1.
It is claimed that a new diet will reduce a person's weight by 4.5 kilograms on average in a period of 2 weeks. The weights of 7 women who followed this diet were recorded before and after the 2-week period. Woman | Weight Before | Weight After 1 | 60.0 | 61.0 2 | 60.5 | 55.0 3 | 62.0 | 58.0 4 | 69.0 | 62.1 5 | 64.5 | 58.5 6 | 62.6 | 60.0 7 | 57.0 | 54.5 Test the hypothesis that the diet reduces a woman's weight by 4.5 kilograms on average against the alternative hypothesis that the mean difference in weight is less than 4.5 kilograms. Use a 0.05 level of significance and assume that the populations to be normally distributed.
A study was done on two groups of overweight individuals. Group 1 was placed on a healthy, moderate diet. Group 2 was not given any diet instructions. After 1 month, the members were asked how many times they engaged in binge eating. The results of the two groups were compared.
The Nature of Probability and Statistics
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