TABLE 7-59 Cholesterol Levels by TreatmentSampleMeanStd DevDiet ProgramCholesterol CholesterolSizeLow carbohydrate225.424.550Conventional75203.821.6 15. A study is conducted to compare mean cholesterolconventional (low-fat, low-calorie) diet for at least6 months. The data are summarized in Table 7-59.levels for individuals following a low-carbohydratediet for at least 6 months to individuals following aonventional (low-fat, low-calorie) diet for at leastk months. The data are summarized in Table 7-59.Test if there is a significant difference in mean cho-lesterol levels between the diet programs using a 5%level of significance.16. Another outcome variable in the study describedin Problem 15 is hypercholesterolemia, defined astotal cholesterol over 220. Among the individualswho follow the low-carbohydrate diet, 56% arehypercholesterolemic, and among the individu-als who follow the conventional diet, 40% arehypercholesterolemic. Test if there is a significantdifference in the proportions using a 5% level ofsignificance.1 characteristics

Answered: TABLE 7-59 Cholesterol Levels by…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 1GP

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Question

TABLE 7-59 Cholesterol Levels by Treatment
Sample
Mean
Std Dev
Diet Program
Cholesterol Cholesterol
Size
Low carbohydrate
225.4
24.5
50
Conventional
75
203.8
21.6

15. A study is conducted to compare mean cholesterol
conventional (low-fat, low-calorie) diet for at least
6 months. The data are summarized in Table 7-59.
levels for individuals following a low-carbohydrate
diet for at least 6 months to individuals following a
onventional (low-fat, low-calorie) diet for at least
k months. The data are summarized in Table 7-59.
Test if there is a significant difference in mean cho-
lesterol levels between the diet programs using a 5%
level of significance.
16. Another outcome variable in the study described
in Problem 15 is hypercholesterolemia, defined as
total cholesterol over 220. Among the individuals
who follow the low-carbohydrate diet, 56% are
hypercholesterolemic, and among the individu-
als who follow the conventional diet, 40% are
hypercholesterolemic. Test if there is a significant
difference in the proportions using a 5% level of
significance.
1 characteristics

Expert Solution

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Hi! Thank you for posting the question. Since you have posted multiple questions, we are answering first question. If you need help with any other question, please re-post the question and mention the part you need help with.

The aim is to check whether there is difference in mean cholesterol levels between the diet programs using a 5% level of significance.

The null and alternative hypotheses are:

Here, µ₁ is the average cholesterol level during low carbohydrate diet, and µ₂ is the average cholesterol level during conventional diet.

$H_{0} : μ_{1} = μ_{2} H_{1} : μ_{1} \neq μ_{2}$

It is assumed that variances are not equal.

The formula for test statistic for non pooled variance is as follows

$t_{c a l c} = \frac{(\bar{x_{1}} - \bar{x_{2}})}{\sqrt{(\frac{s_{1}^{2}}{n_{1}} + \frac{s_{2}^{2}}{n_{2}})}} w h e r e, d f = \frac{{[\frac{s_{1}^{2}}{n_{1}} + \frac{s_{2}^{2}}{n_{2}}]}^{2}}{\frac{{(\frac{s_{1}^{2}}{n_{1}})}^{2}}{n_{1} - 1} + \frac{{(\frac{s_{2}^{2}}{n_{2}})}^{2}}{n_{2} - 1}}$