Exercise 6.12 Let X1,..., Xn be a random sample from Uniform(0, 20). Find theasymptotic distributions of the median, the midquartile range, and Q3, whereQ3 denotes the third quartile and the midquartile range is the mean of the 1stand 3rd quartiles. Compare these three estimates of 0 based on their asymptoticvariances.

Asymptotic distribution An asymptotic distribution is a probability distribution that is…

Answered: Exercise 6.12 Let X1,..., Xn be a…

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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Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The executives hire a statistical consultant and ask her to determine the mean shopping time, μ, of customers at the supermarkets. The consultant will collect a random sample of shopping times at the supermarkets and use the mean of these shopping times to estimate μ. Assuming that the standard deviation of the population of shopping times at the supermarkets is 26 minutes, what is the minimum sample size she must collect in order for her to be 90%confident that her estimate is within 5 minutes of μ? Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements).
Find the F-test statistic to test the claim that the population variances are equal. Both distributions are normal. The standard deviation of the first sample is 3.96014.5373 is the standard deviation of the second sample.
Researchers conducted a study to determine whether magnets are effective in treating back pain. Pain was measured using the visual analog scale, and the results shown below are among the results obtained in the study. Higher scores correspond to greater pain levels. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) to (c) below. Reduction in Pain Level After Magnet Treatment (μ1): n=29, x=0.58, s=0.95 Reduction in Pain Level After Sham Treatment (μ2): n=29, x=0.48, s=1.56 Question content area bottom Part 1 a. Use a 0.05 significance level to test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment (similar to a placebo). What are the null and alternative hypotheses? A. H0: μ1≠μ2 H1: μ1<μ2 B. H0: μ1<μ2 H1:…
Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The mean shopping time, µ, spent by customers at the supermarkets has been reported to be 40 minutes, but executives hire a statistical consultant and ask her to determine whether it can be concluded that u is greater than 40 minutes. To perform her statistical test, the consultant collects a random sample of shopping times at the supermarkets. She computes the mean of these times to be 44 minutes and the standard deviation of the times to be 15 minutes. Based on this information, answer the questions below. What are the null hypothesis (H,) and the alternative hypothesis (H,) that should be used for the test? Hiµ is ? H: p is ? In the context of this test, what is a Type II error? A Type II error is ? fact, u is ? the hypothesis that u is when, in Suppose that the consultant decides not to reject the null hypothesis. What sort of error might she be making?
Researchers conducted a study to determine whether magnets are effective in treating back pain. Pain was measured using the visual analog scale, and the results shown below are among the results obtained in the study. Higher scores correspond to greater pain levels. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) to (c) below. Reduction in Pain Level After Magnet Treatment (μ1): n=27, x=0.46, s=0.89 Reduction in Pain Level After Sham Treatment (μ2): n=27, x=0.42, s= 1.43 * Find the t stat * Find the p value * state the conclusion * Does the confidence interval support the conclusion of the test * Does it appear that magnets are effective in treating back pain? Is it valid to argue that magnets might appear to be effective if the sample sizes are larger? * Is it valid to argue that magnets might appear to be…
The average length of time for students to register in the second semester at a certain university has been 55 minutes. A new registration procedure is being tested. If random samples of 16 students have an average of 50 minutes with standard deviation of 12 minutes under system, can you conclude that the new system is faster than the old one? Assume that the average length of time is normally distributed. Use ά = 0.05.
The table below shows the number of hours per day 11 patients suffered from headaches before and after 7 weeks of soft tissue therapy. At x = 0.01, is there enough evidence to conclude that soft tissue therapy helps to reduce the length of time patients suffer from headaches? Assume the samples are random and dependent, and the population is normally distributed. Complete parts (a) through (f). Patient 8 9 10 11 Q 1 Daily headache hours (before) 2.3 3.4 3.3 2.6 1.8 Daily headache hours (after) 1.8 2.7 1.8 1.6 1.9 1.9 1.2 2.5 2.2 2.0 1.1 2 3 4 5 6 7 4.1 3.2 3.5 2.4 3.7 2.6 C (a) Identify the claim and state Ho and Ha The claim is "The therapy the length of time patients suffer from headaches." Let μd be the hypothesized mean of the patients' daily headache hours before therapy minus their daily headache hours after it. State Ho and H₂. Choose the correct answer below. OA. Ho: Hd=d O C. Ho: Hd ≤0 OB. Ho. Họ sở Ha: Hd >d Ha: Hdd Ha: Hd>0 OD. Ho: Hd #d Ha:Hd=d O E. Ho: Hd zd Ha: Hd 3.169…
Find the F-test statistic to test the claim that the population variances are equal. Both distributions are normal. The standard deviation of the first sample is 2.44628.0027 is the standard deviation of the second sample.
Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The executives hire a statistical consultant and ask her to determine the mean shopping time, μ, of customers at the supermarkets. The consultant will collect a random sample of shopping times at the supermarkets and use the mean of these shopping times to estimate μ. Assuming that the standard deviation of the population of shopping times at the supermarkets is 27 minutes, what is the minimum sample size she must collect in order for her to be 95% confident that her estimate is within 5 minutes of μ? Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements).
Researchers conducted a study to determine whether magnets are effective in treating back pain. Pain was measured using the visual analog scale, and the results shown below are among the results obtained in the s Higher scores correspond to greater pain levels. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) to (c) below. Reduction in Pain Level After Magnet Treatment (u): n=15, x=0.45, s=1.02 Reduction in Pain Level After Sham Treatment (H2): n = 15, x=0.38, s = 1.55 a. Use a 0.01 significance level to test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment (similar to a placebo). What are the null and alternative hypotheses? OA. Ho: H1 H2 H₁₁ 2H2 OC. Ho: HH2 H₁: H₁

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