The cheetah is the fastest land mammal and is highly specialized to run down prey. The cheetah often exceeds speeds of \(60\) mph and according to the online document "Cheetah Conservation in Southern Africa" by J. Urbaniak, the cheetah is capable of speeds up to \(72\) mph. The WeissStats site contains the top speeds in miles per hour, for a sample of \(35\) cheetahs. Use the technology of your choice to do the following tasks.

a. Find a \(95%\) confidence interval for the mean top speed, \(\mu\) of all cheetahs. Assume that the population standard deviation of top speeds is \(3.2\) mph.

b. Obtain a normal probability plot, boxplot, histogram and stem and leaf diagram of the data.

c. Remove the outliers (if any) from the data and then repeat part (a).

d. Comment on the advisability of using the \(z-\)interval procedure on these data.

The speed of cheetah is \(72\) mph.

Compute the \(95%\) confidence interval for the mean top speed,, of all cheetahs by using MINITAB.

MINITAB Procedure:

Step 1: Choose Start > Basic Statistics >\(1\)-Sample \(Z\)

Step 2: In Samples in Column, enter the column of Speed

Step 3: In Standard Deviation, enter \(3.2\)

Step 4: Check Options, enter Confidence level as \(95\)

Step 5: Choose not equalin alternative

Step 6: Click OKin all dialog boxes.

MINITAB output:

One-Sample Z: SPEED

The assumed standard deviation \(=3.2\)

From the MINITAB output, the \(95%\) confidence interval for the mean top speed,\(\mu\), of all cheetahs are \(58.4656\) and \(60.5859\).

Hence, the \(95%\) confidence interval for the mean top speed,\(\mu\), of all cheetahs are lies between \(58.4656\) and \(60.5859\).

The cheetah is capable of speeds up to \(72\) mph

The Weiss stats site contains the top speeds, in miles per hour sample of cheetah is \(35\).

Use Minitab to draw the normal probability Plot for top speed of all cheetahs.

Minitab Procedure:

Step 1: Choose Graph >Probability Plot

Step 2: Choose Singleand then click OK.

Step 3: in Graph Variables, enter the column of Speed

Step 4: click OK.

Minitab output for Normal Probability Plot:

Use Minitab to draw the Boxplot for top speed of all cheetahs.

Minitab Procedure:

Step 1: Choose Graph >Boxplotor Start >EDA >Boxplot

Step 2: under One Y’sChoose Simple, click OK.

Step 3: in Graph Variables, enter the data of Speed

Step 4: click OK.

Minitab output for boxplot:

Use Minitab to draw the Histogram for top speed of all cheetahs.

Minitab Procedure:

Step 1: Choose Graph >Histogram

Step 2: Choose Simple, and then click OK.

Step 3: in Graph Variables, enter the corresponding column of Speed

Step 4: click OK.

Minitab output for Histogram:

Use Minitab to draw the Stem-and-Leaf diagram for top speed of all cheetahs.

Minitab Procedure:

Step 1: Choose Graph >Stem and Leaf

Step 2: Select the Column of Variablesin Graph Variables as Speed

Step 3: Select OK.

Minitab output for Stem-and-Leaf:

Stem-and-leaf of speed \(N=35\)

Leaf Unit \(=1.0\)

Hence, Normal Probability plot, boxplot, histogram, and stem-and-leaf diagram of the data are obtained.

Compute the \(95%\) confidence interval for the mean for top speed of all cheetahs after removing the outliers by using MINITAB.

MINITAB Procedure:

Step 1: Choose Start > Basic Statistics >\(1\)-Sample\(Z\)

Step 2: In Samples in Column, enter the column of Speed

Step 3: In Standard Deviation, enter \(3.2\)

Step 4: Check Options, enter Confidence level as \(95\)

Step 5: Choose not equalin alternative

Step 6: Click OKin all dialog boxes.

MINITAB output:

One-Sample Z: SPEED

The assumed standard deviation \(=3.2\)

From the MINITAB output, the \(95%\) confidence interval for the mean for top speed of all cheetahs is \((57.986, 60.137)\).

Hence, the \(95%\) confidence interval for the mean for top speed of all cheetahs is \((57.986, 60.137)\).

From the given results, it is clear that the mean value with outlier \(59.53\) and the mean value after removing the outlier is \(59.06\). Hence, there is an effect on the mean about \(0.47\). Moreover, and there is same effect on the endpoints of the confidence intervals. Also, the sample size is larger which indicates that the one outlier does not have larger effect.

Hence, there is an effect on the mean about \(0.47\) and there is same effect on the endpoints of the confidence intervals.