Question

CITY	SO2	POP
Phoenix	11	582
Little Rock	15	132
San Francisco	16	716
Denver	24	515
Hartford	82	158
Wilmington	43	80
Washington	30	757
Jacksonville	18	529
Miami	14	335
Atlanta	32	497
Chicago	131	3369
Indianapolis	40	746
Des Moines	20	201
Wichita	10	277
Louisville	35	593
New Orleans	9	361
Baltimore	47	905
Detroit	46	1513
Minneapolis-St. Paul	42	744
Kansas City	18	507
St. Louis	61	622
Omaha	17	347
Albuquerque	15	244
Albany	56	116
Buffalo	11	463
Cincinnati	27	453
Cleveland	80	751
Columbus	27	540
Philadelphia	79	1950
Pittsburgh	63	520
Providence	136	179
Memphis	10	624
Nashville	23	448
Dallas	11	844
Houston	10	1233
Salt Lake City	28	176
Norfolk	38	308
Richmond	38	299
Seattle	40	531
Charleston	40	71
Milwaukee	20	717

Open Pollution data. Test if cities with POPULATION greater than 500 (in thousand) have level of SO2 greater than 28 (ppb) on average.

17. What test/procedure did you perform? (5 points)

• a. One-sided t-test
• b. Regression
• c. Confidence Interval
• d. Two-sided t-test

18. What is the P-value/margin of error? (5 points)

• a. 4.14656E-60
• b. 13.13018
• c. 29.61415
• d. 2.07328E-06
• e. None of these

19. What is the Statistical interpretation? (5 points)

• a. The P-value is much smaller than 5% thus we can claim that the averages are different.
• b. The P-value is much greater than 5% thus we are very certain that the slope is not zero.
• c. The P-value is much greater than 5% thus we cannot claim that the level of SO2 is greater than 28 (ppb) on average.
• d. The prediction interval for the true average level of SO2 for cities with population greater than 500 [26.91528, 53.17563]
• e. None of these.

20. What is the conclusion? (5 points)

• a. We are confident that cities with POPULATION greater than 500 (in thousand) have level of SO2 greater than 25 (ppb) on average.
• b. We are NOT confident that cities with POPULATION greater than 500 (in thousand) have level of SO2 greater than 28 (ppb) on average.
• c. The test is inconclusive and more data is needed.
• d. None of these.

Answer 1

first Take all the observations which have population greater than 500 and save it in the variable so2 to do further testing

17) since we need to test that whether the average level of so2 is greater than 28 and population for those cities which have population greater than 500 which implies it is testing of One-sided t-test.

i.e, option a is correct

18) test is conducted in R and the code is attached

p value for the test is .0471

i.e, option e is correct

19)

Since H0 : average is equal to 28

H1: average is greater than 28

and p value < 0.05 which implies H0 is rejected which implies average is greater than 28 is true

i.e, option e is correct

20) option D is correct since in our test average is greater than 28 for the cities with POPULATION greater than 500 (in thousand)