Question

2. Your own topic: Dallas Cowboys football players

A. Identify a topic of interest to estimate the mean of a population that you would like to set up a confidence interval for: (example – mean weight of the players on the Chicago Bears): Mean weight of the Dallas Cowboys football players.

B. Identify the population you are trying to study.: Dallas Cowboys football players

C. Collect at least 30 sample values from your population for your topic and list the results below. Instead of conducting a “scientific” survey using sound principles of random selection, use a convenience sample consisting of respondents or data that is readily available from your population.

Bradlee Anae

257

Darius Anderson

195

Dorance Armstrong

255

Chidobe Awuzie

202

Blake Bell

252

Francis Bernard

230

Tyler Biadasz

316

Anthony Brown

196

Noah Brown

225

Ventell Bryant

205

Deante Burton

205

Maurice Canady

193

Ron'Dell Carter

269

Jordan Chunn

230

Ha Ha Clinton-Dix

211

La'el Collins

320

Amari Cooper

210

Tyrone Crawford

290

Andy Dalton

220

Trevon Diggs

195

Ben DiNucci

209

Rico Dowdle

215

Ezekiel Elliott

228

Kai Forbath

197

Neville Gallimore

302

Michael Gallup

198

Luke Gifford

243

C.J. Goodwin

190

Stephen Guidry

200

Chris Jones

205

D. Use technology (Excel, statistical calculator website or graphing calculator) to compute the sample mean and sample standard deviation and list them below.

E. Construct a 95% confidence interval for the mean of your sample. (Be sure to use the formulas from section 7.2)

F. Identify the shortcomings of using a convenience sample, and try to identify how a sample of subjects randomly selected form the population might be different.

Answer 1

D) Here, we have to use technology (Excel, statistical calculator website or graphing calculator) to compute the sample mean and sample standard deviation and list them below.

Steps to perform the mean and standard deviation in excel is-

1. Enter the values in a single column.

2. Select the data and click on formula tab.

3. Select the mean and standard deviation formula from statistical option and enter the range of the column here A1 to A30.

4. Click OK.

After running the above steps we get,

mean = 228.77

standard deviation = 37.86

E) Here we have to construct a 95% confidence interval for the mean of your sample.

Formula:

which is obtained from t-distribution table.

So, (228.77-37.86*2.045/5.477,228.77+37.86*2.045/5.477)

= (214.63,242.90)

F) Let us consider the hypothesis,

H₀: µ = 0 vs H₁: µ ≠ 0

The test statistic used is –      

where, n is the sample number = 30

                 µ₀ is the population mean = 0

                  s is the sample standard deviation

                   is the sample mean

where,   = 228.77

= 37.86

Therefore, T = 5.477(228.77-0)/37.86 = 33.1

The critical value is

which is obtained from t-distribution table.

Now we reject the null if |T| > 2.045. So here, |T|>2.045 so we reject the null and conclude that, the sample of subject randomly selected are not different from the population.