Test Ho-Proportion

11.A air quality instrument logs 0 when standards are not met and 1 when standards are met. The log data is below

Time Air Quality Time Air Quality

0:00:00 1 0:12:30 1

0:00:30 0 0:13:00 1

0:01:00 1 0:13:30 1

0:01:30 1 0:14:00 1

0:02:00 0 0:14:30 1

0:02:30 1 0:15:00 1

0:03:00 1 0:15:30 0

0:03:30 1 0:16:00 0

0:04:00 1 0:16:30 0

0:04:30 1 0:17:00 1

0:05:00 1 0:17:30 1

0:05:30 1 0:18:00 1

0:06:00 1 0:18:30 1

0:06:30 1 0:19:00 1

0:07:00 1 0:19:30 1

0:07:30 1 0:20:00 1

0:08:00 1 0:20:30 1

0:08:30 1 0:21:00 1

0:09:00 0 0:21:30 0

0:09:30 1 0:22:00 1

0:10:00 1 0:22:30 0

0:10:30 1 0:23:00 1

0:11:00 1 0:23:30 1

0:11:30 1

0:12:00 1

First, compute the proportion meeting standards as the mean of Air Quality values. Second, at alpha = 0.10 (sensitive, exploratory), test the hypothesis that proportion of times that air quality meets standards is at least 90%.

A.The pvalue of 0.966 indicates that the data provide insignificant evidence against H0: 0.90. H0 is not rejected at \alpha=0.10. The status quo remains unchanged

B. None of the answers are correct

C. The pvalue of 0.022 indicates that the data provide strong evidence against H0: 0.90. H0 is rejected at =0.10. The status quo has changed.

D. The pvalue of 0.062 indicates that the data provide weak evidence against H0: 0.90. H0 is rejected at =0.10.

E. The pvalue of 0.006 indicates that the data provide overwhelming evidence against H0: 0.90. H0 is rejected at =0.10. Send out an air quality alert.

HINT: The sample proportion is the mean of the Air Quality values. Compute the mean to 4 decimal place accuracy. Test H0: 0.90.

Test H0-Mean

12.The Lawnpoke Golf Association(LGA) has established rules that manufacturers of golf equipment must meet for their products to be acceptable for LGA events. BatOutaHell Balls uses a proprietary process to produce balls with a mean distances of 295 yards. BatOuaHell is concerned that is the mean distance falls below 295 yards, the word will get out and sales will sag. Further, if the mean distance exceeds 295 yards, their balls may be rejected by LGA. Measures of the distance are listed below

Yards

290

272

277

287

274

305

288

297

307

284

272

280

293

279

303

295

292

289

279

At =0.05, test the no action hypothesis that the balls have a mean distance of 295 yards.

A. The test statistic is 1.297 and the critical value is 1.734, therefore the test statistics is less than the critical value and the null hypothesis is not rejected. The distance is about 295 yards.

B. The test statistic is 1.908 is greater than the critical value of 1.734, therefore H0 is rejected. It is reasonable to assume that the distance is not 295 yards.

C. The test statistic is 2.238 is greater than the critical value of 1.734, therefore H0 is rejected. It is reasonable to assume that the distance is not 295 yards.

D. The test statistic is 13.003 and the critical value is 1.734, therefore the test statistics is greater than the critical value of 1.734 and the null hypothesis is rejected. The distance is not 295 yards.

HINT:

Test H0: =295

HA: = 295

Test H0-Paired Data

13.The Fast N' Hot food chain wants to test if their "BOGO" program increases customer traffic enough to support the cost of the program. For each of 15 stores, one day is selected at random to record customer traffic with the program in effect, and one day is selected at random to record customer traffic with program not in effect. The results are below

Customer Traffic

With Program Without Program

144 140

236 233

108 110

43 42

337 332

134 135

148 151

30 33

181 178

146 147

159 162

248 243

150 149

54 48

349 346

For each store, compute the different = traffic with program minus traffic without program. At =0.05, test the hypothesis that the mean difference is at most 0 (at best the program makes no difference, or worse it decreases traffic), against the alternative that the mean difference >0 (the program increases traffic.

A. the pvalue rejects H0:mean difference>0

B. the pvalue of 0.033 provides strong evidence against H0. H0 is rejected at=0.05. You decide to recommend further evaluation of the program.

C. the pvalue of 0.084 provides weak evidence against H0. H0 is not rejected at =0.05. You decide the evidence is not strong enough to recommend further evaluation of the program

D. the pvalue of 0.221 indicates that the data provide insignifance evidence against H0. H0 is not rejected at =0.05. You decide to conclude the study and not to recommend the program.

E. None of the answers are correct

F. the pvalue of 0.002 provides overwhelming evidence against H0. H0 is rejected at =0.05. You decide that the program results in increased customer traffic, overall, and recommend the program be implement.

HINT: Is this paired data (dependent on the unit observation), or data from independent populations?

Test H0-Mean

14.BigDeal Real Estate surveyed prices per square foot in the valley and foothills of Hoke-a-mo, Utah. BD's results are below

Valley Foothills

109 75

116 154

106 156

157 105

147 215

105 130

173 219

153 193

137 147

110 169

Based on the results, are prices per square foot equal at =0.01?

A. The critical value is 2.977 since the two-tailed scenario. The test statistic is 1.936. Since the test statistic < the critical value, the test statistic does not lie in the area of rejection. Do not reject the null hypothesis. The prices per square foot are equal at alpha =0.01

B. The critical value is 2.977 since the two-tailed scenario. The test statistic is 1.513. Since the test statistic < the critical value, the test statistic does not lie in the area of rejection. Do not reject the null hypothesis. The prices per square foot are equal at alpha =0.01

C. The critical value is 2.977 since the two-tailed scenario. The test statistic is 2.239. Since the test statistic < the critical value, the test statistic does not lie in the area of rejection. Do not reject the null hypothesis. The prices per square foot are equal at alpha =0.01

D. The critical value is 2.977 since the two-tailed scenario. The test statistic is 3.207. Since the test statistic < the critical value, the test statistic does lie in the area of rejection. Reject the null hypothesis. The prices per square foot are not equal at alpha =0.01

HINT: Is this paired data (2 measurement dependent on the unit of observation), or data from 2 independent populations?