Excel Lab: Finding the Margin of Error

Problem 1 - Any Smartphones for Sale?

A random sample of the newest model of Samsung Galaxy smartphones being sold over the Internet had the following prices, in dollars:

199 169 385 329 269 149 135 249 349 299 249

Corporate executives at Samsung would like to estimate the mean price of all Samsung Galaxy smartphones being sold over the Internet. So, we will construct a confidence interval to estimate the population mean price of all Samsung Galaxy smartphones of the latest version being sold over the Internet.

1.Explain why it is necessary to check whether the population is approximately normal before constructing a confidence interval.

2.Construct a box plot of these data using Excel. This box plot should be on your Excel file with appropriate formatting and labels.

3.Is it reasonable to assume that this sample came from a normal population? Explain.

4.Use Excel to find summary statistics (including the margin of error for a 95% confidence interval) for this data set using the Descriptive Statistics command in the Data Analysis options under the Data menu. On your Excel file in the summary statistics you just obtained, highlight the point estimate in yellow and the margin of error in green.

5. Show how to find the boundaries of a 95% confidence interval using only the highlighted values from your summary statistics output. (For this activity, do not use any other methods to find the confidence interval.)

6. Write an interpretation for your confidence interval, including units if appropriate. You may round the upper and lower limits to 2 places.

Add a new worksheet to your Excel file for problem 2.

Problem 2 - Eat your Cereal

Boxes of cereal are labeled as containing 14 ounces. Following are the weights, in ounces, of a sample of 12 boxes:

14.02 13.97 14.11 14.12 14.10 14.02 14.15 13.97 14.05 14.04 14.11 14.12

The quality control manager is concerned that the mean weight is actually less than 14 ounces. Your help is needed once again to construct a confidence interval to estimate the mean weight of all boxes of cereal of this type. It is reasonable to assume that the population is approximately normal.

1. Explain why it is not necessary to assess normality for this sample, even though it is a small sample.

2. Use Excel to find summary statistics (including the margin of error for a 98% confidence interval) for this data set using the Descriptive Statistics command in the Data Analysis options under the Data menu. On your Excel file in the summary statistics you just obtained, highlight the point estimate in yellow and the margin of error in green.

3. Show how to find the boundaries of a 98% confidence interval using only the highlighted values from your summary statistics output. (For this activity, do not use any other methods to find the confidence interval.)

4. Write an interpretation for your confidence interval, including units if appropriate. You may round the upper and lower limits to 2 places.

5. Based on the confidence interval, is there a reason the quality control manager should be concerned that the mean weight is actually less than 14 ounces? Explain.

Add a new worksheet to your Excel file for problem 3.

Problem 3 - Football Players

The weights (in pounds (lb)) of 52 randomly selected NFL football players are presented below.

305 265 287 285 290 235 300 230 195 236 244 194 190

307 218 315 265 210 194 216 255 300 315 190 185 183

313 246 212 201 308 270 241 242 306 237 315 215 200

295 187 204 257 185 255 318 230 316 200 324 245 185

We would like to construct a 90% confidence interval for the mean weight of NFL football players.

1. Explain why it is not necessary to assess normality for this sample.

2. Use Excel to find summary statistics (including the margin of error for a 90% confidence interval) for this data set using the Descriptive Statistics command in the Data Analysis options under the Data menu. On your Excel file in the summary statistics you just obtained, highlight the point estimate in yellow and the margin of error in green.

3. Show how to find the boundaries of a 90% confidence interval using only the highlighted values from your summary statistics output. (For this activity, do not use any other methods to find the confidence interval.)

4. Write an interpretation for your confidence interval, including units if appropriate. You may round the upper and lower limits to the nearest whole number.

5. Does the confidence interval estimate the mean weight for the sample of 52 NFL players or for the population of NFL players? Explain.

Add a new worksheet to your Excel file for problem 4.

Problem 4 - Big Salary for the Boss

Following is the total compensation, in millions of dollars, for Chief Executive Officers (CEOs) at 20 large U.S. corporations in a recent year.

2.75 9.15 2.32 23.84 13.12 9.91 6.39 2.19 4.28 0.70

3.18 8.20 1.68 4.64 6.05 6.59 11.31 1.35 25.84 2.85

A research firm would like to analyze the mean compensation of CEOs in the U.S. and has decided to construct a 99% confidence interval to estimate the mean compensation amount.

1. Explain why it is necessary to check whether the population is approximately normal before constructing a confidence interval.

2. Construct a box plot of these data using Excel. This box plot should be on your Excel file with appropriate formatting and labels.

3. Is it reasonable to assume that this sample came from a normal population? Explain.

4. If appropriate, construct a 99% confidence interval for the mean compensation of a CEO in the U.S. using Excel procedures similar to those used in the previous problems. If it is not appropriate to construct the confidence interval, then explain why it is not appropriate.