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3. The "Atkins Diet" is a diet where one eats predominantly protein and very few carbohydrates. A nutritionist would like to estimate the proportion of students at a small school who have heard of the Atkins diet. The school has a total of N = 1000 students. The nutritionist selects a stratified sample of students from the school. Stratum 1 consists of male students. Stratum 2 consists of female students. The total number of male students at the school is N, = 600, and the total number of female students is N, = 400. Independent simple random samples are selected from the two strata. The nutritionist uses proportional allocation to determine the sample sizes for the strata. The total sample size for the survey is n = 200. The sample proportion of males who have heard of the Atkins diet is p, = 0.85. The sample proportion of females who have heard of the Atkins diet is p2 = 0.75. a. What are the sample sizes for the two strata? (Hint: remember that proportional allocation is used.) b. Consider only the female stratum. Construct a 95% confidence interval for the proportion of female students who have heard of the Atkins diet. c. Estimate the overall proportion of students at the school who have heard of the Atkins diet.

3. The "Atkins Diet" is a diet where one eats predominantly protein and very few carbohydrates. A nutritionist would like to estimate the proportion of students at a small school who have heard of the Atkins diet. The school has a total of N = 1000 students. The nutritionist selects a stratified sample of students from the school. Stratum 1 consists of male students. Stratum 2 consists of female students. The total number of male students at the school is N, = 600, and the total number of female students is N, = 400. Independent simple random samples are selected from the two strata. The nutritionist uses proportional allocation to determine the sample sizes for the strata. The total sample size for the survey is n = 200. The sample proportion of males who have heard of the Atkins diet is p, = 0.85. The sample proportion of females who have heard of the Atkins diet is p2 = 0.75. a. What are the sample sizes for the two strata? (Hint: remember that proportional allocation is used.) b. Consider only the female stratum. Construct a 95% confidence interval for the proportion of female students who have heard of the Atkins diet. c. Estimate the overall proportion of students at the school who have heard of the Atkins diet.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 25PPS
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3. The "Atkins Dieť" is a diet where one eats predominantly protein and very few carbohydrates. A nutritionist would like to estimate the proportion of students at a small school who have heard of the Atkins diet. The school has a total of N = 1000 students. The nutritionist selects a stratified sample of students from the school. Stratum 1 consists of male students. Stratum 2 consists of female students. The total number of male students at the school is N = 600, and the total number of female students is N2 = 400. Independent simple random samples are selected from the two strata. The nutritionist uses proportional allocation to determine the sample sizes for the strata. The total sample size for the survey is n = 200. The sample proportion of males who have heard of the Atkins diet is p1 = 0.85. The sample proportion of females who have heard of the Atkins diet is p2 = 0.75. a. What are the sample sizes for the two strata? (Hint: remember that proportional allocation is used.) b. Consider only the female stratum. Construct a 95% confidence interval for the proportion of female students who have heard of the Atkins diet. c. Estimate the overall proportion of students at the school who have heard of the Atkins diet.
Transcribed Image Text:3. The "Atkins Dieť" is a diet where one eats predominantly protein and very few carbohydrates. A nutritionist would like to estimate the proportion of students at a small school who have heard of the Atkins diet. The school has a total of N = 1000 students. The nutritionist selects a stratified sample of students from the school. Stratum 1 consists of male students. Stratum 2 consists of female students. The total number of male students at the school is N = 600, and the total number of female students is N2 = 400. Independent simple random samples are selected from the two strata. The nutritionist uses proportional allocation to determine the sample sizes for the strata. The total sample size for the survey is n = 200. The sample proportion of males who have heard of the Atkins diet is p1 = 0.85. The sample proportion of females who have heard of the Atkins diet is p2 = 0.75. a. What are the sample sizes for the two strata? (Hint: remember that proportional allocation is used.) b. Consider only the female stratum. Construct a 95% confidence interval for the proportion of female students who have heard of the Atkins diet. c. Estimate the overall proportion of students at the school who have heard of the Atkins diet.
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