You create a new hypothesis test on data X1,... , X100 with the null assumptions that theyare Normally distributed with mean 10 and variance 4. You decide to use a custom hypothesistest withX – 10Фp-valueV4/100Recall that X is the sample mean of the data. You will reject the test if p-value < 0.01.(a) What is the type I error rate of this test?(b) If X1,..., X100 are normally distributed with mean 11 and variance 4, what is the typeII error rate of this test?(c) If X1,..., X100 are normally distributed with mean 9 and variance 16, what is the type•• )II error rate of this test?

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Answered: You create a new hypothesis test on…

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 sample of size 11 produced a variance of 18. Is this sufficient to reject the null hypothesis that σ2 = 6 when tested using a 0.05 level of significance?
Consider a hypothesis test with H 0: μ = 20 vs H 1: μ ≠ 20) at α = 0.05 on mean of a Normal population with unknown variance. If the sample variance is 4 and the true mean is 18.5, then the sample size required to obtain a power of test at least 80% is close to 15 using an appropriate OC curve. True False
From a sample of 25 observations, the estimate of the variance of the population was found to be 15.0 From another sample of 14 observations, the estimate variance was found to be 9.7 Can we accept the hypothesis that the two samples come from populations with equal variance, or must we conclude that the variance of the second population is smaller? Use the 0.01 level of significance.
A sample of 16 items from population 1 has a sample variance of 5.4 and a sample of 20 items from population 2 has a sample variance of 2.4. Test the following hypotheses at the 0.05 level of significance.
An automobile manufacturer claims that their van has a 59.4 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this van. After testing 17 vans they found a mean MPG of 59 with a variance of 2.89 MPG. Is there sufficient evidence at the 0.1 level that the vans underperform the manufacturer's MPG rating? State the null and alternative hypotheses for the above scenario.
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 Ho and H1 the alternative hypothesis that we would use for this test. Ho:? H1:?
A carpenter is making doors that are 2058 millimeters tall. If the doors are too long they must be trimmed, and if they are too short they cannot be used. A sample of 28 doors is made, and it is found that they have a mean of 2069millimeters with a variance of 900. Is there evidence at the 0.05 level that the doors are either too long or too short? State the null and alternative hypotheses for the above scenario.
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:____
In building an arena, steel bars with a mean ultimate tensile strength of 400 Megapascal (MPa) with a variance of 81 MPa were delivered by the manufacturer. The project engineer tested 50 steel bars and found out that the mean ultimate tensile strength is 390 MPa. The decision for the extension of the contract with the manufacturer depends on the engineer. Test the hypothesis whether or not there is no significant difference between the two means using a two-tailed test with α = 0.01.
A carpenter is making doors that are 2058 millimeters tall. If the doors are too long they must be trimmed, and if they are too short they cannot be used. A sample of 61 doors is made, and it is found that they have a mean of 2044 millimeters with a variance of 729. Is there evidence at the 0.05 level that the doors are either too long or too short? State the null and alternative hypotheses for the above scenario.
In building an arena, steel bars with a mean ultimate tensile strength of 400 Megapascal (MPa) with a variance of 81 MPa were delivered by the manufacturer. The project engineer tested 50 steel bars and found out that the mean ultimate tensile strength is 390 MPa. The decision for the extension of the contract with the manufacturer depends on the engineer. Test the hypothesis whether or not there is no significant difference between the two means using a two-tailed test with α = 0.01. What are the appropriate hypotheses for the two-tailed test? What is the test statistic to be used and the reasons for its selection? What is the critical value c? What is the value of the test statistic or the computed value? Formulate a conclusion about the given situation.

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