Suppose that a random variable X has a probability density function given as2 (B - x)B²0

A quantity is said to be pivotal quantity if it's distribution is free from parameter of interest.

Answered: i) Use an appropriate method to show…

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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Your company manufactures hot water heaters. The life spans of your product are known to be normally distributed with a mean of 13 years and a standard deviation of 1.5 years. You want to set the warranty on your product so that you do not have to replace more than 5% of the hot water heaters that you sell. How many years should you claim on your warranty? A) 12.91 B) 15.47 C) 22.88 D) 10.53 E) 13.09
A. Determine test statistic B. Determine critical value with k-1 degree of freedom then use the chi square to find the critical value for this part. C. Reject H0 or Fail H0.
Assume that both populations are normally distributed. a) Test whether u >H2 at the a = 0.01 level of significance for the given sample data. b) Construct a 99% confidence interval about u - 42- Sample 1 28 52.6 Sample 2 23 44.1 9.4 O A. Ho: H1 H2 O B. Ho: H1 = H2, H:Hq H2, HHy H2 Determine the test statistic. t= (Round to two decimal places as needed.) Approximate the P-value. Choose the correct answer below. O A. P-value 20.10 O B. P-value <0.01 O C. 0.05 s P-value <0.10 O D. 0.01 SP-value <0.05 Should the hypothesis be rejected at the a = 0.01 level of significance? V the null hypothesis because the P-value is V the level of significance. b) The confidence interval is the range from to (Round to twwo decimal places as needed. Use ascending order
p = proportion of graduates who get a jobA published article indicates that only 1 in 3 university graduates have a job waiting for them. In an investigation of 200 recent graduates of university A, it was found that 51 had a job. Can it be concluded, with a level of significance of 0.01, that from this university the proportion of graduates who have a job is lower? Choose 1. the correct conclusion2. the correct interpretationSelect one: a) 1. H0 is rejected2. It can be ensured, with 99% confidence, that less than a third of the graduates of said university get a job. b) 1. H0 is not rejected2. It can be ensured, with 99% confidence, that less than a third of the graduates of said university get a job. c) 1. H0 is not rejected2. There is not enough evidence to consider, with 99% confidence, that less than a third of the graduates of said university get a job. d) 1. H0 is rejected2. There is not enough evidence to consider, with 99% confidence, that less than a third of the graduates of…
7.) A sample of weights of 30 four-year-old boys had a standard deviaCon of 8.6 lbs. Can we claim that they have the same standard deviaCon as girls, which is 7.8 lbs? Test using ∝= 0.05 and a.) a hypothesis test b.) an appropriate confidence interval
A) State the hypothesis for this test B) construct a 95 % confidence interval about the sample mean of stocks traded in 2014 C) will the researcher reject the null hypothesis
Suppose that the mean cranial capacity for men is 1190 cc (cubic centimeters) and that the standard deviation is 300 cc. Assuming that men's cranial capacities are normally distributed, complete the following statements. (a) Approximately 99.7% of men have cranial capacities between I cc and cc. (b) Approximately ? of men have cranial capacities between 590 cc and 1790 cc.
Assume that both populations are normally distributed. a) Test whether u > H2 at the a = 0.01 level of significance for the given sample data. b) Construct a 99% confidence interval about u - 42. 177 Sample 1 24 51.7 9.5 Sample 2 43.1 99 O A. Ho: H1 = H2, H:Hq>H2 O B. Ho: H1 = H2, HH1H2, H1: H1 H2 Determine the test statistic. %3D (Round to two decimal places as needed.) Approximate the P-value. Choose the correct answer below. O A. P-value 20.10 O B. P-value <0.01 O C. 0.01 s P-value <0.05 O D. 0.05 s P-value <0.10 Should the hypothesis be rejected at the a = 0.01 level of significance? V the null hypothesis because the P-value is the level of significance. b) The confidence interval is the range from to (Round to two decimal places as needed. Use ascending order.)
Exercise 1: You are interested in determining the average number of social media accounts people have. You interview 30 people at random and the number of social media accounts they have has a sample mean of 7.1 and a sample standard deviation of 2.09. a) b) Define the parameter of interest. State and check if the assumptions needed for constructing the appropriate CI for the parameter of interest are satisfied. c) Find a 90% confidence interval for the parameter defined in part a). Use the table, not the calculator to find the appropriate critical value. d) Write a sentence to interpret the CI computed in part c).
1. Assume that the populations are normally distributed. Test the hypothesis that a, >o, at the a-0.01 level of significance for the given sample data. Population 1: n, 61, 5,-34.4 Population 2, n, = 31, 3,-27.6 A) Test statistic: F=1.55. Critical value -4.31. Do not reject H, B) Test statistic:F-6.89. Critical value =4.31. Reject H.. -C) Test statistic: F-2.96. Critical value =2.21. Reject H OTest statistic: F-1.55. Critical value -2.21. Do not reject H,. 23
4. In the past, the mean running time for a certain type of cell phone battery has been 19.2 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has increased as a result. The hypotheses are: Họ: u=19.2 hours H1: µ>19.2 hours Explain the meaning of a Type I error. A) Concluding that u> 19.2 hours when in fact u = 19.2 hours B) Concluding that u 19.2 hours C) Concluding that u = D) Concluding that u> 19.2 hours when in fact u> 19.2 hours 19.2 hours when in fact u > 19.2 hours

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i) Use an appropriate method to show that W = is a pivotal quantity. ii) Construct a 90% upper confidence limit for ß, using part i)