Inference of the population mean with small samples Show development for the solution In an clinic, a certain group of people is on a program to lose weight and improve their health. At the end of the program and as a result of a random sample of 10 patients, it was obtained that the average weight loss was 15.9 with a standard deviation of 5.3. a) Construct a 95% confidence interval for the population mean of the weight loss program. b) If the clinic expects people to lose an average of 14 kilograms with the program, do you think the program is adequate? justifies c) What sample size would you recommend the clinic use if they want to have a confidence level of 99% and a margin of error of 2 kilograms?

Inference of the population mean with small samples Show development for the solution In an clinic, a certain group of people is on a program to lose weight and improve their health. At the end of the program and as a result of a random sample of 10 patients, it was obtained that the average weight loss was 15.9 with a standard deviation of 5.3. a) Construct a 95% confidence interval for the population mean of the weight loss program. b) If the clinic expects people to lose an average of 14 kilograms with the program, do you think the program is adequate? justifies c) What sample size would you recommend the clinic use if they want to have a confidence level of 99% and a margin of error of 2 kilograms?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

Data indicates that adolescent girls tend to experience a drop in self-esteem. To evaluate this result, a researcher obtains a sample of N = 36 adolescent girls, all 13 years old. A self-esteem measure is administered to each participant and the average score for the sample is X =68. It is known that the distribution of self-esteem scores for the population of pre-teen girls is normal with mean 80 and standard deviation 10. (a) Compute a 95% confidence interval for µ, the population mean self-esteem score for adolescent girls. (b) Compute Cohen’s d to estimate the size of the described effect. (c) Perform a hypothesis test to decide whether the mean self-esteem score for adolescent girls is significantly different from the mean self-esteem score for pre-teen girls. (d) Compute and interpret a Bayes factor for the model (either H0 or H1) with the best predictive adequacy. (e) Compute and interpret the posterior model probability for the winning model chosen in part (d).
10 In a test of the effectiveness of garlic for lowering cholesterol, 44 subjects were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes (before−after) in their levels of LDL cholesterol (in mg/dL) have a mean of 3.4 and a standard deviation of 18.8. Construct a 95% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL cholesterol? What is the confidence interval estimate of the population mean μ? (?) mg/dL<μ<(?) mg/dL (Round to two decimal places as needed.) What does the confidence interval suggest about the effectiveness of the treatment? A. The confidence interval limits contain 0, suggesting that the garlic treatment did not affect the LDL cholesterol levels. B. The confidence interval limits do not contain 0, suggesting…
If a Type I error is made, what conclusion will be drawn regarding the mean breaking strength?
Q2) Independent-Samples t-Test (Round calculated results to the hundredth (2nd place to the right of the decimal)) In a research project, researchers collected demographic and health data from a sample of elderly residents in the community. To examine any possible gender differences in their sample, they want to see if the females and the males differ significantly on the education level (number of years of formal schooling). The researchers are not predicting any direction in the possible gender differences so the hypotheses should be non-directional. They would like to run a two-tailed test with α = .10. Male Subject ID Education Female Subject ID Education 1 14 13 14 2 15 14 15 3 17 15 18 4 13 16 18 5 15 17 16 6 15 18 17 7 13 19 16 8 15 20 16 9 15 21 17 10 16 22 15 11 17…
The ages of registered voters in Smith County are normally distributed with a population standard deviation of 3 years and an unknown population mean. A random sample of 18 voters is taken and results in a sample mean of 55 years. Find the margin of error for a 95% confidence interval for the population mean. z0.10z0.10 z0.05z0.05 z0.025z0.025 z0.01z0.01 z0.005z0.005 1.282 1.645 1.960 2.326 2.576 You may use a calculator or the common z values above. Round the final answer to two decimal places.
Suppose you sample six people on their number of visits to Chick-fil-A in a month given by variable Y. Y = 3,6,7,10,15,19 (A) What is the mean of Y? Standard Deviation of Y?(B) What is the Standard Error of Y?(C) Construct 90% and 95% Confidence Intervals for Y.
HO A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before treatment, 20 subjects had a mean wake time of 102.0 min. After treatment, the 20 subjects had a mean wake time of 93.1 min and a standard deviation of 22.4 min. Assume that the 20 sample values appear to be from a normally distributed population and construct a 99% confidence interval estimate of the mean wake time for a population with drug treatments. What does the result suggest about the mean wake time of 102.0 min before the treatment? Does the drug appear to be effective? Construct the 99% confidence interval estimate of the mean wake time for a population with the treatment. min < u< min (Round to one decimal place as needed.) - E nd
The probability that Paul’s train to work is late on any day is 0.15, independently of other days. (i) The number of days on which Paul’s on which Paul’s train to work is late during a 450-days period is denoted by the random carriable Y. Find a value of a such the P(Y>a)≈ 1/6 . In the expansion of (0.15+0.85)^50 , the terms involving 0.15^r and 0.15^(r+1) and denoted by Tr and Tr+1 respectively. (ii) Show that Tr / Tr+1 = 17(r+1)/3(50-r)
In a psychological experiment, 36 people (subjects) are selected randomly. The variableof interest is their reaction time to a particular stimulus (in seconds). Historical datastates that the variance in reaction times is 4 sec2and that the distribution of reactiontimes is approximately normal. The average time for the randomly selected subjects is6.2 seconds. What is the point estimate of this study? Based on this information, construct a 99% confidence interval for themean reaction time. Interpret the confidence interval that you obtained in (b).
Select all of the assumptions that you need to make when creating a confidence interval on the difference between means. At least 2% of the population sampled Independently sampled values Homogeneity of variance Normally distributed populations?
True or False? A researcher wants to be sure the mean difference in the change in blood pressure has a margin of error no more than 5 points and the difference in the standard deviation between the mean blood pressure points from the first medication used to treat high blood pressure and the second medication used to treat high blood pressure is 14 points. The desired sample size required to ensure a 95% confidence interval for the proposed study used to compare the efficacy of two medications used to treat high blood pressure during a cross-over trial is n = 31.
A study of the career paths of hotel general managers sent questionnaires to an SRS of 280 hotels belonging to major U.S. hotel chains. There were 157 responses. The average time these 157 general managers had spent with their current company was 13.28 years. (Take it as known that the standard deviation of time with the company for all general managers is 3 years.) (a) Find the margin of error for an 80% confidence interval to estimate the mean time a general manager had spent with their current company: years (b) Find the margin of error for a 99% confidence interval to estimate the mean time a general manager had spent with their current company: years