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Q. 8.101

Expert-verifiedFound in: Page 334

Book edition
9th

Author(s)
Weiss, Neil

Pages
590 pages

ISBN
9780321989505

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.

Part a. The \(95%\) confidence interval for the mean top speed,, of all cheetahs are \((58.4656, 60.5859)\)

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

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

Part d. There is an effect on the mean about \(0.47\) and there is same effect on the endpoints of the confidence intervals**.**

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 equal **in **alternative**

Step 6: Click **OK **in 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 **Single **and 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 >Boxplot **or **Start >EDA >Boxplot**

Step 2: under **One Y’s **Choose **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 Variables **in 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 equal **in **alternative**

Step 6: Click **OK **in 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.

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