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Q. 8.101

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Elementary Statistics
Found in: Page 334
Elementary Statistics

Elementary Statistics

Book edition 9th
Author(s) Weiss, Neil
Pages 590 pages
ISBN 9780321989505

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Short Answer

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.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Part a. Step 1. Given information

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

Part a. Step 2. Calculation

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 \(60.5859\).

Part b. Step 1. Given information

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 \(35\).

Part b. Step 2. Calculation

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.

Part c. Step 1. Calculation

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 \((57.986, 60.137)\).

Part d. Step 1. Calculation

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.

Most popular questions for Math Textbooks

The value of a statistic used to estimate a parameter is called a ______ of the parameter.

Suppose that a simple random sample is taken from a normal population having a standard deviation of 10 for the purpose of obtaining a 95% confidence interval for the mean of the population.

a. If the sample size is 4 , obtain the margin of error.

b. Repeat part (a) for a sample size of 16

c. Can you guess the margin of error for a sample size of 64 ? Explain your reasoning.

For a t-curve with df=21, find each f-value, and illustrate your results graphically.

a. The t-value having an area 0.10 to its right

b. t0 a 1

c. The t-value has an area 0.025 to its left (Hint: A t-curve is symmetric at about 0.)

d. The two t-values that divide the area under the curve into a middle 0.90 area and two outside areas of 0.05

State True or False. Give Reasons for your answers.

The margin of error can be determined if you know only the length of the confidence interval.

Poverty and Dietary Calcium. Refer to Exercise 8.70

a. Determine and interpret a 95% upper confidence bound for the mean calcium intake of all people with incomes below the poverty level.

b. Compare your one-sided confidence interval in part (a) to the (twosided) confidence interval found in Exercise 8.70
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