A survey was taken of the heights, in inches, of 20- to 29-year-old males. A sim

Question

A survey was taken of the heights, in inches, of 20- to 29-year-old males. A simple random sample of n = 16 males 20 to 29 years old results in the data in the table. Construct a 95% t-interval about the population mean. For convenience, a normal probability plot and boxplot are given. Decide if a 95% t-interval can be constructed about the population mean. If not, state the reason why. A t-interval can be constructed. A t-interval cannot be constructed because there is an outlier. A t-interval cannot be constructed because the data is not normal. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. The 95% confidence interval is (, ). (Round to two decimal places as needed.) The interval cannot be found.

Explanation / Answer

The correct answer is A ) t interval can be constructed

Because from the probability plot (or QQ plot ) all the points lies in the interval and also from the box plot the data follows approximately normally distributed.

When data comes from normal distribution and we don't know the sample size then we can used t-interval .

b) t confidence interval for data

using Minitab

Here population standard deviation is not given and we have sample data set so we can used one sample t interval to construct the confidence interval for popuation mean.

Step 1) enter the given data set in minitab columns

Step 2) Stat>>>Basic Statistics >>1 sample t...

Click on "Samples in columns"

select the column name in which your data is present.

then click on Option select level of confidence = 95

Alternative " not equal"

Click on Ok

Again "click on OK"

then we get the following output

One-Sample T: X

Variable N Mean StDev SE Mean 95% CI
X 15 69.100 3.574 0.923 (67.12, 71.08)

From the above output the 95% confidence for population mean is (67.12, 71.08)

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