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# Let X equal the Brinell hardness measurement of ductile

ISBN: 9780321923271 41

## Solution for problem 3E Chapter 8.1

Probability and Statistical Inference | 9th Edition

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Problem 3E

PROBLEM 3E

Let X equal the Brinell hardness measurement of ductile iron subcritically annealed. Assume that the distribution of X is N(μ, 100). We shall test the null hypothesis H0: μ = 170 against the alternative hypothesis H1:μ > 170, using n = 25 observations of X.

(a) Define the test statistic and a critical region that has a significance level of α = 0.05. Sketch a figure showing this critical region.

(b) Arandom sample of n = 25 observations of X yielded the following measurements:

Calculate the value of the test statistic and state your conclusion clearly.

(c) Give the approximate p-value of this test.

Step-by-Step Solution:
Step 1 of 3

PSYCH STATS POWERPOINT 9 ● t statistic ● when we set a = .05, this result will only occur at random 5% of the time ○ we are 95% sure our result didn’t occur by chance ● df = (n-1) ● standard error indicates the variability in M ● we use z-scores to test our hypothesis ● with t-statistics, we don’t have certain information ● confidence intervals = give us an idea of how well our numbers are at estimating the values ● we rarely know the SD ○ we use “s” to estimate the standard deviation ■ the sample standard deviation has sampling variability ● t-statistic = used to test hypotheses about a

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Let X equal the Brinell hardness measurement of ductile