The heights of a simple random sample of 400 male high school sophomores in aMidwestern state are measured. The sample mean is x = 66.2 inches. Suppose that theheights of male high school sophomores follow a Normal distribution with a standarddeviation of o= 4.1 inches. Suppose the heights of a simple random sample of 100male sophomores were measured rather than 400. Which of the following statements istrue?A) The margin of error for the 95% confidence interval would increase.B) The margin of error for the 95% confidence interval would decrease.C) The margin of error for the 95% confidence interval would stay the same becausethe level of confidence has not changed.D) The standard deviation owould decrease.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The time to travel to school for high school students in South Bend is known to have a normal distribution with a standard deviation of o = 15 minutes. You take a simple random sample of 40 South Bend high school students students, and their average time to travel to school is 25 minutes. Find the 90% confidence interval for the population mean time. O A. (21.91, 28.09) B. (21.96, 28.04) O C. (21.00, 29.00) D. (21.10, 28.90)
The distribution of study times for first-year students follow a Normal distribution with a standard deviation σ = 48 minutes. Suppose a sample of 344 students found that the mean study time for these students was x¯= 170 minutes per week. Use this to find a 94.38% confidence interval to estimate the mean study time for all students. We are 94.38% confident that the mean study time for first-year students is between the following ( answer) minutes and ( answer) minutes. The answer needs to be the mean study time for first-year students is between what amount of minutes and the following minutes.
A study of 40 English professors showed that they spend, on average, 12.6 minutes correcting a student's term paper. The standard deviation was 2.5 minutes. Construct the 99% confidence interval of the mean for all term papers.
The standard deviation, S, for the annual medical cost of 24 households was found to equal $1689 find a 95% confidence interval for the standard deviation of the annual medical cost for all households. Assume medical costs are normally distributed.
In a random sample of 5 mobile devices, the mean repair cost was $60.00 and the standard deviation was $12.00. Assume the population is normally distributed and use a t-distribution to find the margin of error and construct a 95% confidence interval for the population mean. Interpret the results.
The com reported the medical doctors’ salary level. The mean salary for the doctor is $250,000 and standard deviation of $100,000. Find the following probabilities assuming that doctor’s salary has a normal distribution. Suppose we don’t have any information about population, and from a sample of 100 doctors, we find the sample mean salary was $255,000 with the standard deviation of $99,500. What is the 95% confidence interval? Based on the standard deviation of $100,000 and allow the margin of errors to $20,000, what is your sample size should be at 95% confidence level.
In a random sample of 17 people, the mean commute time to work was 30.2 minutes and the standard deviation was 7.1 minutes. Assume the population is normally distributed and use a t- distribution to construct a 95% confidence interval for the population mean y. What is the margin of error of y? Interpret the results.
Assume that distances people driving to work are normally distributed. In a random sample of five people, the mean driving distance to work was 23 miles and the standard deviation was 6 miles. What is the length of the 95% confidence interval for the mean driving distance to work. Round to the nearest mile.
A researcher is conducting a study to determine the mean trough dosage of medication for a population. Assume a previous study was conducted for the same medication and the mean trough dose was found to be 490 mg with a standard deviation of 30 mg. If the researcher wants to be 95% confident the true mean trough dosage of the medication is within 10 mg of the true mean trough dosage, what sample size is needed if the study is predicted to have an 76% retention rate? n = 50 n = 71 n = 47 n = 104

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