Question

All the procedures should be done with 5% P-value or 95% confidence interval.Some answers are approximated, choose the most appropriate answer. Open Pollution data. SETUP: Since wind clears the air, some people believe that the cities with wind speed above 10 have less SO2 than the cities with wind speed below 10. Given the data your job is to decide if this is a reasonable expectation. I. What test/procedure did you perform? (6.66 points) a. One sided T-test b. Two sided T-test c. Regression d. Confidence interval II. Statistical interpretation? (6.66 points) a. Since P-value is small we are confident that the slope is not zero. b. Since P-value is small we are confident that the averages are different. c. Since P-value is too large the test is inconclusive. d. None of these. III. Conclusion? (6.66 points) a. Yes, this is a reasonable expectation. b. No, we cannot confirm that this is a reasonable expectation.

CITY	SO2	WIND
Phoenix	11	6
Charleston	40	6.5
Cincinnati	27	7.1
Richmond	38	7.6
Nashville	23	7.9
Little Rock	15	8.2
Louisville	35	8.3
New Orleans	9	8.4
Columbus	27	8.6
San Francisco	16	8.7
Salt Lake City	28	8.7
Jacksonville	18	8.8
Albany	56	8.8
Albuquerque	15	8.9
Denver	24	9
Hartford	82	9
Wilmington	43	9
Miami	14	9
Atlanta	32	9.1
Memphis	10	9.2
Washington	30	9.3
Pittsburgh	63	9.4
Seattle	40	9.4
St. Louis	61	9.5
Baltimore	47	9.6
Philadelphia	79	9.6
Indianapolis	40	9.7
Kansas City	18	10
Detroit	46	10.1
Chicago	131	10.4
Minneapolis-St. Paul	42	10.6
Providence	136	10.6
Norfolk	38	10.6
Houston	10	10.8
Omaha	17	10.9
Cleveland	80	10.9
Dallas	11	10.9
Des Moines	20	11.2
Milwaukee	20	11.8
Buffalo	11	12.4
Wichita	10	12.7

Answer 1

I. Since some people believe that the cities with wind speed above 10 have less SO2 than the cities with wind speed below 10, so we divide the whole data of SO2 into parts: One part consists of SO2 corresponding to the wind speed below 10 and the other part consists of SO2 corresponding to the wind speed above and equal to 10 and verifying the believe of people we use b. Two sided T-test.

Assume the normality assumptions hold.

Test and CI for Two Variances: Wind <10, Wind>=10

Method

Null hypothesis Sigma(Wind <10) / Sigma(Wind>=10) = 1
Alternative hypothesis Sigma(Wind <10) / Sigma(Wind>=10) not = 1
Significance level Alpha = 0.05

Statistics

Variable N StDev Variance
Wind <10 27 20.157 406.311
Wind>=10 14 43.298 1874.747

Ratio of standard deviations = 0.466
Ratio of variances = 0.217

Test
Method DF1 DF2 Statistic P-Value
F Test (normal) 26 13 0.22 0.001

Since p-value<0.001 so we can't assume the two population variances are same.

Now we perform two sided T test with unequal variances.

Two-Sample T-Test and CI: Wind <10, Wind>=10

Two-sample T for Wind <10 vs Wind>=10

N Mean StDev SE Mean
Wind <10 27 34.2 20.2 3.9
Wind>=10 14 42.1 43.3 12

Difference = mu (Wind <10) - mu (Wind>=10)
Estimate for difference: -8.0
95% lower bound for difference: -29.4
T-Test of difference = 0 (vs >): T-Value = -0.65 P-Value = 0.738 DF = 15
II Option c. Since P-value is too large the test is inconclusive.

III. Option b. No, we cannot confirm that this is a reasonable expectation.