Let the following sample of 8 observations be drawn from a normal population wit

Question

Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation: 16, 21, 12, 23, 25, 26, 22, 17. Use Table 2.

a. Calculate the sample mean and the sample standard deviation. (Round intermediate calculations to 4 decimal places. Round "Sample mean" to 3 decimal places and "Sample standard deviation" to 2 decimal places.)

b. Construct the 90% confidence interval for the population mean. (Round "t" value to 3 decimal places and final answers to 2 decimal places.)

Confidence interval             to

c. Construct the 90% confidence interval for the population mean. (Round "t" value to 3 decimal places and final answers to 2 decimal places.)

Confidence interval             to

Sample mean Sample standard deviation

Explanation / Answer

a. For the given data

mean=Sumx/n=20.25

Create the following table.

Find the sum of numbers in the last column to get.

=sqrt((xiX¯)^2/n1)4.83

b. Now t table value for 90% CI at n-1=7 df is 1.895

So Margin of Error=E=t*(/sqrt(n))=3.24

Hence CI=mean+-E=20.25 +-3.24=(17.01,23.49)

c. It would be same as b

data data-mean (data - mean)2 16 -4.25 18.0625 21 0.75 0.5625 12 -8.25 68.0625 23 2.75 7.5625 25 4.75 22.5625 26 5.75 33.0625 22 1.75 3.0625 17 -3.25 10.5625

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