The town of Westville, Kansas boasts that the mean height of its population is t

Question

The town of Westville, Kansas boasts that the mean height of its population is the largest of any town in the United States. Easton, Texas claim is greater than that of Westville. A random sample is taken of the adults in both towns. In Westville, the sample of 41 adults had a mean height of 78 inches with a standard deviation of 5.7 inches; while in Easton the sample of 46 adults had a mean height of 81 inches with a standard deviation of 6.1 inches. Perform a significance test at ? 0.05 to determine if the mean height of Westville's population is shorter than that of Easton. State the hypotheses, find the test statistic and critical value, and state your conclusion 3. s that the mean height of its population

Explanation / Answer

Ho: muKansas=muTexas

Ha: muTexas>muKansas

So here to check the same we need ot find the t-stat as we have sample sd is known

t=( (X1bar-X2bar)-(mu1-mu2) ) / ( sqrt(sd1/n1+sd2/n2) )

t = (81-78)/(sqrt(6.1/46 + 5.7/41) = 5.756121

while from the t table tck values at 5% conf interval is 1.662978 at (n1+n2-2 = 85 df)

And so t calculated > tck  

We need to reject the Ho and hence we conclude that mean height of texas is more than mean height of Kansas

Hope the above ans has helped you in understanding the problem. Pls upvote if it has really helped you. Good Luck!!

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