Two independent random samples have been selected, 100 observations frompopulation 1 and 120 from population 2. Sample means x1 = 60 and x2 = 50 wereobtained. From previous experience with these populations, it is known that thevariances are o,? = 64 and o,? = 100. Test the claim that the difference in the meansof the 2 populations is equal to 5. Use a=0.02.(1) Critical Values (Round off to 3 decimal places):(2) Test Statistic (Round off to 2 decimal places):(3) Conclusion:(Type 'Reject HO' or 'Fail to Reject HO')

Given : Claim : The difference in the means of the 2 populations is equal to 5.

Answered: Two independent random samples have…

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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Suppose X and Y are two random variables with covariance Cov(X, Y) = 3 and Var(X) = 16. Find the correlation coefficient between X and Y.
The records of a casualty insurance company show that, in the past, its clients have had a mean of 1.7 auto accidents per day with a variance of 0.0025. The actuaries of the company claim that the variance of the number of accidents per day is no longer equal to 0.0025. Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis H and the alternative hypothesis H, that we would use for this test. H0:__H 1:__
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The records of a casualty insurance company show that, in the past, its clients have had a mean of 1.8 auto accidents per day with a variance of 0.0016. The actuaries of the company claim that the variance of the number of accidents per day is no longer equal to 0.0016. Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis H0 and the alternative hypothesis H1 that we would use for this test. Ho:____ H1:____
You have been asked to determine if two different production processes have different mean numbers of units produced per hour. Process 1 has a mean de- fined as µ1 and process 2 has a mean defined as µ2.The null and alternative hypotheses are as follows:H0 :µ1 - µ2 ≤ 0H1 :µ1 - µ2 > 0The process variances are unknown but assumed to be equal. Using random samples of 25 observations from process 1 and 36 observations from process 2, the sample means are 56 and 50 for populations 1 and 2, respectively. Can you reject the null hypothesis using a probability of Type I error α = 0.05 in each case?a. The sample standard deviation from process 1 is 30 and from process 2 is 28.b. The sample standard deviation from process 1 is 22 and from process 2 is 33.c. The sample standard deviation from process 1 is 30 and from process 2 is 42.d. The sample standard deviation from process 1 is 15 and from process 2 is 36.
As we noted previously, even a very small effect can be significant if the sample is large enough. Suppose, for example, that a researcher obtains a correlation of r = .60 for a sample of n =10 participants. Is this sample sufficient to conclude that a significant correlation exists in the population? Use a two-tailed test with α = .05. Based on the previously provided correlation, would you reject the null hypothesis established
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The records of a casualty insurance company show that, in the past, its clients have had a mean of 1.9 auto accidents per day with a variance of 0.0036. The actuaries of the company claim that the variance of thenumber of accidents per day is no longer equal to 0.0036. Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis H0 and the alternative hypothesis H1 that we would use for this test.
As we have noted in previous chapters, even a very small effect can be significant if the sample is large enough. Suppose, for example, that a researcher obtains a correlation (computed from the raw data) of r = 0.60 for a sample of n = 10 participants. (4 pts. total) Is this sample sufficient to conclude that a significant correlation exists in the population? Use a two-tailed test with α = .05. In your response, be sure to specify the critical value for r.

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