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Test 3 study guide

Test 3 study guide - 1 The mass Department of labor would...

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1. The mass. Department of labor would like an estimate of the avg. weekly unemployment benefi in mass. They obtain a sample of 45 unemployed workers currently receiving benefits and find the sample average (x bar) is $228 with a sample standard deviation (s) of $52. a. Do you know that the sample mean (x bar) is normally distributed? Explain why or why not Since n=45 >30 we can rely on the C.L.T. to know that x bar is normal b. Find a 95% confidence interval for the average weekly unemployment benefit in Mass. (x bar) [plus and minus ] t(s/(sqrt(n))) 228 [plus and minus] 2.015368(52/(sqrt(45))) 228 [plus and minus] 15.62253 212.3775-243.6225 T= TINV(.05, 45) or .01 for 99% c. in the context of this problem, explain the meaning of the results for part b. The mass. Dept. of labor can be 95% confident that the average unemployment benefit for all workers is at least $212.38, but not more than $243.62 2. A random survey of 350 adults found that 195 of them do not exercise regulary. a. Do you know that the sample proportion (p) is normally distributed? Explain why or why not. Since n π =np=x=195≥10 And N(1- π )=n(1-p)=n-x= 155≥10 X is symmetric so p is normal.
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