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Testing of hypothesis - logical questions

Need clarification regarding the questions below - thank you in advance.

1. The manager of the quality department for a tire manufacturing company wants to know the average tensile strength of rubber used in making a certain brand of radial tire. The population is normally distributed and the population standard deviation is known. She uses a Z test to test the null hypothesis that the mean tensile strength is 800 pounds per square inch. The calculated Z test statistic is a positive value that leads to a p-value of .009 for the test. If the significance level () is .01, the null hypothesis would be rejected. TRUE

The level of significance indicates the probability of rejecting a false null hypothesis. FALSE
5. When conducting a hypothesis test about a single mean, other relevant factors held constant, increasing the level of significance from .05 to .10 will decrease the probability of a Type II error. TRUE

Given the following information about a hypothesis test of the difference between two means based on independent random samples, what is the standard deviation of the difference between the two means? Assume that the samples are obtained from normally distributed populations having equal variances.
H0: A ≤ B, and H1: A > B X ̅ 1 = 12, X ̅ 2 = 9, s1= 5, s2 = 3, n1 =15, n2 =14.
A. 2.039
B. 1.546 xxxxx
C. 1.792
D. 4.159
E. 2.389
. Which if any of the following statements about the chi-square test of independence is false?
A. If ri is row total for row i and cj is the column total for column j, then the estimated expected cell frequency corresponding to row i and column j equals (ri) (cj)/n
B. The test is valid if all of the estimated cell frequencies are at least five
C. The alternative hypothesis states that the two classifications are statistically independent
D. The chi-square statistic is based on (r-1)(c-1) degrees of freedom where r and c denote, respectively the number of rows and columns n the contingency table

Solution Preview

1. The manager of the quality department for a tire manufacturing company wants to know the average tensile strength of rubber used in making a certain brand of radial tire. The population is normally distributed and the population standard deviation is known. She uses a Z test to test the null hypothesis that the mean tensile strength is 800 pounds per square inch. The calculated Z test statistic is a positive value that leads to a p-value of .009 for the test. If the significance level () is .01, the null hypothesis would be rejected.
Yes, it is TRUE because the p-value is less than the 0.01 level of significance so we will reject the null ...

Solution Summary

This solution is comprised of a detailed explanation of testing of hypothesis. This solution mainly discussed the different types of tests, level of significance, decision rule, type I and type II errors.

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