9.4.20-T -Question Help * Listed below are the heights of candidates who won ele

Question

9.4.20-T -Question Help * Listed below are the heights of candidates who won elections and the heights of the candidates with the next highest number of votes. The data are in chronological order, so the corresponding heights from the two lists are matched. Assume that the paired samle data are simple random samples and that the dne ences have a dstribu on that is approxi mately normal Construct a 9 % confidence inte al estimate of the mean of the population of all 'winnenrunne-up differences. Does height appear to be an important factor in winning an election? winner 75 71 69 71 72 787770 Runner-Up 74 69 6770 7373 71 Construct the 95% confidence interval. (Subtract the height of the runner-up from the height of the winer to find the diference, d.)

Explanation / Answer

here sample size n=8, is less than 30 and we use t-value for confidence interval

(1-alpha)*100% confidence interval for population mean difference=sample difference±t(alpha/2,n-1)*sd/sqrt(n)

mean difference =0.7875
sd=1.7150
n=8

95% confidence interval =mean±t(0.05/2, n-1)*sd/sqrt(n)

(second part)  

(1-alpha)*100% confidence interval for population mean difference=sample difference±t(alpha/2,n-1)*sd/sqrt(n)

(third part)

t-value lower limit upper limit 95% confidence interval 2.36 -0.65 2.22

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