Question

CITY	SO2
Phoenix	11
Little Rock	15
San Francisco	16
Denver	24
Hartford	82
Wilmington	43
Washington	30
Jacksonville	18
Miami	14
Atlanta	32
Chicago	131
Indianapolis	40
Des Moines	20
Wichita	10
Louisville	35
New Orleans	9
Baltimore	47
Detroit	46
Minneapolis-St. Paul	42
Kansas City	18
St. Louis	61
Omaha	17
Albuquerque	15
Albany	56
Buffalo	11
Cincinnati	27
Cleveland	80
Columbus	27
Philadelphia	79
Pittsburgh	63
Providence	136
Memphis	10
Nashville	23
Dallas	11
Houston	10
Salt Lake City	28
Norfolk	38
Richmond	38
Seattle	40
Charleston	40
Milwaukee	20

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

Given that,
population mean(u)=28
sample mean, x =36.902
standard deviation, s =29.799
number (n)=41
null, Ho: μ=28
alternate, H1: μ>28
level of significance, alpha = 0.05
from standard normal table,right tailed t alpha/2 =1.684
since our test is right-tailed
reject Ho, if to > 1.684
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =36.902-28/(29.799/sqrt(41))
to =1.913
| to | =1.913
critical value
the value of |t alpha| with n-1 = 40 d.f is 1.684
we got |to| =1.913 & | t alpha | =1.684
make decision
hence value of | to | > | t alpha| and here we reject Ho
p-value :right tail - Ha : ( p > 1.9128 ) = 0.03147
hence value of p0.05 > 0.03147,here we reject Ho
ANSWERS
---------------
17.
one sided t test
null, Ho: μ=28
alternate, H1: μ>28
test statistic: 1.913
critical value: 1.684
decision: reject Ho
18.
p value
option:none
p-value: 0.03147
19.
p value is less than 5%
20.
option:a
we have enough evidence to support the claim that if cities with POPULATION greater than 500 (in thousand)
have level of SO2 greater than 28 (ppb) on average.