Answer
A 95% confidence interval is \[\left( 33.1667,\text{ }43.6667 \right)\]
Work Step by Step
A 95% confidence interval is calculated in Minitab as follows:
Step 1: Enter the provided data into column C1.
Step 2: Go to\[\text{Calc}\to \text{Random data }\!\!~\!\!\text{ }\to \text{Sample from Columns}\]
After this, enter the values in the pop-up window as shown below:
Number of rows to sample – 12,000
From columns – “Crawling Babies”
Store samples in – C2
Step 3: Select sample with replacement and click OK.
Step 4: Again go to \[\text{Calc}\to \text{Make patterned data }\!\!~\!\!\text{ }\to \text{Simple set of numbers}\]
After this, enter the values in pop-up window as shown below:
Store patterned data in – C3
From first value – 1
To last value – 1000
Number of times to list each value – 12
Number of times to list the sequence – 1
Step 5: After entering the values as shown above, click OK.
Step 6: Go to\[\text{Statistics }\!\!~\!\!\text{ }\to \text{Basic Statistics}\to \text{Store Descriptive Statistics}\]
Select C2 in the Variables textbox and C3 in the by-variables textbox. After this, click on statistics and select mean and click OK two times.
Step 7: Go to\[\text{Data}\to \text{Sort }\!\!~\!\!\text{ }\]
After this, select mean1 in the sort column textbox and by column textbox. Also, store the sorted data in the new worksheet.
Step 8: From the output, the 2.5th percentile or 25th observation is 33.1667 and 97.5th percentile or 975th observation is 43.6667. The lower and upper bound of the confidence interval is 33.1667 and 43.6667, respectively.
The 95% confidence interval using bootstrap method is \[\left( 33.1667,\text{ }43.6667 \right)\] and its width is 10.5. The 95% confidence interval using t-interval is \[\left( 31.90,\text{ 44}\text{.60} \right)\] and its width is 12.7. Now, the width of the t-interval is 12.7 and the width of the bootstrap confidence interval is 10.5 at 95% confidence level, so it can be said that the bootstrap method gives better interval than t-interval.
