7. The drying time of a type of paint under specified test conditions is known to be normallydistributed with a mean value of 75 min and a stand ard deviation of 9 min. Chemists haveprop osed a new additive desinged to decrease aver age drying time. It is believed that dryingtimes with this ad ditive will remain normally distributed with o = 9. Bec ause of the expenseas sociated with the additive, evidence should strongly suggest an improvement in average dry-ing time before such a conclusion is adopted. Let u denote the true aver age drying time whenthe additive is used. The appropriate hypotheses are Ho : H = 75 versus Ha : µ < 75.Suppose that we take a sample of n = 25 test specimens. We would reject the null hypothesisif the sample me an a from this sample is less than 71.5 minutes.(a)Find the value of a, the probability of a type I error, for this test.Find the value of B(70), the probability of a type II error when the true value(b)of μ= 70.

Given that sample size n = 25 Population SD = 9 Rejection region is that reject the null hypothesis…

Answered: Find the value of a, the probability of…

Find the value of a, the probability of a type I error, for this test. Find the value of B(70), the probability of a type II error when the true value of u = 70.

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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Concept explainers

Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.

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7. The drying time of a type of paint under specified test conditions is known to be normally
distributed with a mean value of 75 min and a stand ard deviation of 9 min. Chemists have
prop osed a new additive desinged to decrease aver age drying time. It is believed that drying
times with this ad ditive will remain normally distributed with o = 9. Bec ause of the expense
as sociated with the additive, evidence should strongly suggest an improvement in average dry-
ing time before such a conclusion is adopted. Let u denote the true aver age drying time when
the additive is used. The appropriate hypotheses are Ho : H = 75 versus Ha : µ < 75.
Suppose that we take a sample of n = 25 test specimens. We would reject the null hypothesis
if the sample me an a from this sample is less than 71.5 minutes.
(a)
Find the value of a, the probability of a type I error, for this test.
Find the value of B(70), the probability of a type II error when the true value
(b)
of μ= 70.

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