Question

In: Statistics and Probability

The National Weight Control Registry tries to mine secrets of success from people who lost at...

The National Weight Control Registry tries to mine secrets of success from people who lost at least 30 pounds and kept it off for at least a year. It reports that out of 3500 registrants, 922 were on a low-carbohydrate diet (less than 90 grams a day).

a. Develop a 99% confidence interval for the proportion of people in the registry on a low-carb diet.

b. Is it possible that this population proportion is 25%?

c. For a follow-up study, how large a sample is needed to estimate the proportion within .5% and with 99% confidence?

(Please make sure you focus on the numbers given above)

Expert Solution

a.Develop a 99% confidence interval for the proportion of people in the registry on a low-carb diet

We need to construct the 9% confidence interval for the population proportion. We have been provided with the following information about the number of favorable cases:

Favorable Cases X =	922
Sample Size N =	3500

The sample proportion is computed as follows, based on the sample size N = 3500 and the number of favorable cases X = 922

The critical value for α=0.01 is z_c = 2.576. The corresponding confidence interval is computed as shown below:

b. Is it possible that this population proportion is 25%?

As the interval contains 0.25, hence yes it is possible that this population proportion is 25%

c. For a follow-up study, how large a sample is needed to estimate the proportion within .5% and with 99% confidence?

The critical value for α=0.01 is z_c = 2.576

Margin of error, E = 0.5% = 0.005

n = 9972.3653

n = 9973

orchestra answered 2 years ago

Jan is a 75-year old woman who has lost significant weight in the last year. She...

Jan is a 75-year old woman who has lost significant weight in the last year. She has complaints of anorexia and joint pain. She states she just doesn’t feel like eating sometimes. She has had significant constipation causing hemorrhoids and states it is very difficult to stool. - What other medical history is necessary in order to effectively treat Jan? - What education might be helpful? - What are complications you might consider? - What therapies might benefit Jan's health?

A medical statistician wants to estimate the average weight loss of people who are on a...

A medical statistician wants to estimate the average weight loss of people who are on a new diet plan. In a study, he guesses that the standard deviation of the population of weight losses is about 20 pounds. How large a sample should he take to estimate the mean weight loss to within 8 pounds from the sample average weight, with 95% confidence? Is your estimation always correct? Please briefly explain your reasoning. If you start with a bigger sample,...

A national caterer determined that 36% of the people who sampled their food said that it...

A national caterer determined that 36% of the people who sampled their food said that it was delicious. A random sample of n=144 people is obtained from a large population. The 144 people are asked to sample the caterer's food. What is the probability that more than 34% thought the food was delicious? Question 20 options: A) 0.6915 B) 0.5987 C) 0.3085 D) 0.4013 Question 19 (1 point) A national caterer determined that 36% of the people who sampled their...

Recently, several cars in the local neighborhood Winding Hills have lost control and fallen from the...

Recently, several cars in the local neighborhood Winding Hills have lost control and fallen from the road into a lake below. The homeowner’s association has asked for your advice regarding a plan to install a barrier at the site of the frequent accidents to keep cars from falling into the lake. The barrier company has provided the HOA with a variety of potential materials to make the barrier from. One member of the HOA, Sal, has recommended selecting the cheapest...

PYTHON You need to control the number of people who can be in an oyster bar...

PYTHON You need to control the number of people who can be in an oyster bar at the same time. Groups of people can always leave the bar, but a group cannot enter the bar if they would make the number of people in the bar exceed the maximum of 100 occupants. Write a program that reads the sizes of the groups that arrive or depart. Use negative numbers for departures. After each input, display the current number of occupants....

What are the arguments of the people who advocate for planned economy non-democratic approach to national...

What are the arguments of the people who advocate for planned economy non-democratic approach to national development? 400 words

Provide an appropriate response. Many people think that a national lobby's successful fight against gun control...

Provide an appropriate response. Many people think that a national lobby's successful fight against gun control legislation is reflecting the will of a minority of Americans. A random sample of 4000 citizens yielded 2250 who are in favor of gun control legislation. a) Show that this situation meets the necessary criteria to calculate the confidence interval for the proportion. b) Estimate the true proportion of all Americans who are in favor of gun control legislation using a 90% confidence interval....

The producer of a weight-loss pill advertises that people who use the pill lose, after one...

The producer of a weight-loss pill advertises that people who use the pill lose, after one week, an average (mean) of 1.85 pounds with a standard deviation of 0.95 pounds. In a recent study, a group of 45 people who used this pill were interviewed. The study revealed that these people lost a mean of 1.77 pounds after one week. If the producer's claim is correct, what is the probability that the mean weight loss after one week on this...

A nurse is the preparing to transfer a client who is partially weight bearing from the...

A nurse is the preparing to transfer a client who is partially weight bearing from the bed to chair .Which of the following actions should the nurse take ? A : Keep his knees straight when moving the client B: Position the chair next to bed at 90 angle C: Have the client bear weight on her stronger leg D: Stand with his feet together when lifting the client 2: A nurse is preparing to insert a peripheral IV catheter...

What is the impact on people who are descended from ancestors who experience involuntary migration.