A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, \( \bar{x} \), is found to be 114, and the sample standard deviation, s, is found to be 10.(a) Construct a 95% confidence interval about \( \bar{x} \) if the sample size, n, is 25.(b) Construct a 95% confidence interval about \( \bar{x} \) if the sample size, n, is 29.(c) Construct a 96% confidence interval about \( \bar{x} \) if the sample size, n, is 25.(d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed?

Given that simple random sample of size n is drawn from a population that is normally distributed.…

Answered: A simple random sample of size n is…

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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A certain counselor wants to compare mean IQ scores for two different social groups. A random sample of 15 IQ scores from group 1 showed a mean of 117 and a standard deviation of 17 , while an independently chosen random sample of 9 IQ scores from group 2 showed a mean of 112 and a standard deviation of 15 . Assuming that the populations of IQ scores are normally distributed for each of the groups and that the variances of these populations are equal, construct a 90% confidence intervalfor the difference −μ1μ2 between the mean μ1 of IQ scores of group 1 and the mean μ2 of IQ scores of group 2 . Then find the lower limit and upper limit of the 90% confidence interval. Carry your intermediate computations to at least three decimal places. Round your responses to at least two decimal places. (If necessary, consult a list of formulas.)
A random sample of 42 KU college students gave a mean age of their vehicles of 11.3 years and a standard deviation of 3.4 years. A separate random sample of 38 KU college employees gave a mean vehicle age of 9.2 years with a standard deviation of 3.1 years. Find a 90% confidence interval for the difference in the population mean of vehicle ages between students and employees, u1-u2. Use students as the first population.
A random sample of 1000 people was taken and a 95% confidence interval for the average income in thousands is (30, 70). What would be a 90% confidence interval based on the same sample? Assume the population standard deviation \sigmaσ is known.
A cell phone manufacturer has hired you to estimate the population mean of the battery lifetimes for all phones of their latest model. You decide to measure battery lifetime by recording the time it takes for the battery charge to run out while a tester is streaming videos on the phones continuously. Then you select a random sample of 45 cell phones of the manufacturer's latest model and record their battery lifetimes. Assume that the population standard deviation of the battery lifetimes for that cell phone model (using your method of measurement) is 2.42 hours. Based on your sample, follow the steps below to construct a 95% confidence interval for the population mean of the battery lifetimes for all phones of the manufacturer's latest model. (If necessary, consult a list of formulas.) (a) Click on "Take Sample" to see the results from your random sample of 45 phones of the manufacturer's latest model. Take Sample Sample size: 0 Number of phones Point estimate: 0 45 Sample mean…
A cell phone manufacturer has hired you to estimate the population mean of the battery lifetimes for all phones of their latest model. You decide to measure battery lifetime by recording the time it takes for the battery charge to run out while a tester is streaming videos on the phones continuously. Then you select a random sample of 45 cell phones of the manufacturer's latest model and record their battery lifetimes. Assume that the population standard deviation of the battery lifetimes for that cell phone model (using your method of measurement) is 2.42 hours. Based on your sample, follow the steps below to construct a 95% confidence interval for the population mean of the battery lifetimes for all phones of the manufacturer's latest model. (If necessary, consult a list of formulas.) (a) Click on "Take Sample" to see the results from your random sample of 45 phones of the manufacturer's latest model. Take Sample Sample size: Number of phones Point estimate: 45 Sample mean Standard…
A random sample of 41 adult coyotes in a region of northern Minnesota showed the average age to be x = 2.09 years, with sample standard deviation s = 0.88 years. However, it is thought that the overall population mean age of coyotes is ? = 1.75. Do the sample data indicate that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years? Use ? = 0.01. (a) State the null and alternate hypotheses.(Select the correct one) H0: ? = 1.75 yr; H1: ? ≠ 1.75 yr H0: ? > 1.75 yr; H1: ? = 1.75 yr H0: ? = 1.75 yr; H1: ? > 1.75 yr H0: ? = 1.75 yr; H1: ? < 1.75 yr (b) What is the value of the sample test statistic? Round your answer to three decimal places. (c) Estimate the P-value. (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??(Selet which one is correct) We fail to reject the null hypothesis because the p-value is greater than ? = 0.01.…
The average score that can be obtained on a standardized test at your school is114with a standard deviation of 16. You are a reporter for the school newspaper and you want to know if thetypical deviation, o,Student athletes are different. To find out, he surveys a random sample of 18student athletes and determines that for the sample, the mean score is112with a standard deviation of 12.If we assume that the scores that the student athletes obtained follow an approximately normal distribution, is there enough evidence to conclude, at the significance level of0.05, which standard deviation is higher among student athletes? Perform a two-tailed test. Then complete the following. Carry intermediate calculations to three or more decimal places. (If necessary, you can refer to a list of formulas .) (to) Formulate the null hypothesish and the alternative hypothesish 1' ho: p = 16 0 (b) (c) (d) h :p # 16 1 Determine which type of test statistic to use. chi-square Z you chi-square Degrees of…
In the past, a chemical company produced 880 pounds of a certain type of plastic per day. Now, using a newly developed and less expensive process, the mean daily yield of plastic for the first 50 days of production is 871 pounds; the standard deviation is 21 pounds. Do the data provide sufficient evidence to indicate that the mean daily yield for the new process is less than that of the old procedure? (Use α{=0.05) (a) Alternative hypothesis for the problem above is
The average score that can be obtained on a standardized test at your school is114with a standard deviation of 16. You are a reporter for the school newspaper and you want to know if thetypical deviation, o,Student athletes are different. To find out, he surveys a random sample of 18student athletes and determines that for the sample, the mean score is112with a standard deviation of12.If we assume that the scores that the student athletes obtained follow an approximately normal distribution, is there enough evidence to conclude, at the level of significance of 0.05, which standard deviation is higher among student athletes? Perform a two-tailed test. Then complete the following. Carry intermediate calculations to three or more decimal places. (If necessary, you can refer to a list of formulas .) (to) Formulate the null hypothesish and the alternative hypothesish 1' ho: 0 0 (b) (c) (d) h ! 1 0 Determine which type of test statistic to use. (Choose an option) Find the value of the test…
If the random variable x is normally distributed with a mean of 88 and a standard deviation of 12, then P(X >=96) is equal to ?
Suppose we want to test the hypothesis that mothers with low socioeconomic status (SES) deliver babies whose birth weights are different from normal. To test this hypothesis, a random sample of 100 birth weights is selected from a list of full-term babies of SES mothers. The mean birth weight is found to be 115 oz. Suppose the average birth weight of all babies (based on nationwide surveys of millions of deliveries) is known to be 120 oz with = 24 oz. Set = .05 Assume all conditions are met, what is the p-value of their test? Give your answer to 4 decimal places.
A random sample of 14 items is drawn from a population whose standard deviation is unknown. The sample mean is I = 780 and the sample standard deviation is s= 5. Use Appendix D to find the values of Student'st (a) Construct an interval estimate of u with 98% confidence. (Round your answers to 3 decimal places.) The 98% confidence interval is from to (b) Construct an interval estimate of u with 98% confidence, assuming that s= 10. (Round your answers to 3 decimal places.) The 98% confidence interval is from to (c) Construct an interval estimate of u with 98% confidence, assuming that s = 20. (Round your answers to 3 decimal places.) The 98% confidence interval is from to (d) Describe how the confidence interval changes as s increases. O The interval stays the same as s increases. O The interval gets wider as s increases. O The interval gets narrower as s increases. < Prev 6 of 10 NAxt 耳C a re to search

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