Question

In what follows use any of the following tests/procedures: Regression, multiple regression, confidence intervals, one sided T-test or two sided T-test. 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.

link to data set: https://www.limes.one/Content/DataFiles/Cars04.txt

CITY    SO2     MANUF   POP     TEMP    WIND    PRECIP-INCHES   PRECIP-#DAYS
Phoenix 11      213     582     70.3    6       7.05    36
Little Rock     15      91      132     61      8.2     48.52   100
San Francisco   16      453     716     56.7    8.7     20.66   67
Denver  24      454     515     51.9    9       12.95   86
Hartford        82      412     158     49.1    9       43.37   127
Wilmington      43      80      80      54      9       40.25   114
Washington      30      434     757     57.3    9.3     38.89   111
Jacksonville    18      136     529     68.4    8.8     54.47   116
Miami   14      207     335     75.5    9       59.8    128
Atlanta 32      368     497     61.5    9.1     48.34   115
Chicago 131     3344    3369    50.6    10.4    34.44   122
Indianapolis    40      361     746     52.3    9.7     38.74   121
Des Moines      20      104     201     49      11.2    30.85   103
Wichita 10      125     277     56.6    12.7    30.58   82
Louisville      35      291     593     55.6    8.3     43.11   123
New Orleans     9       204     361     68.3    8.4     56.77   113
Baltimore       47      625     905     55      9.6     41.31   111
Detroit 46      1064    1513    49.9    10.1    30.96   129
Minneapolis-St. Paul    42      699     744     43.5    10.6    25.94   137
Kansas City     18      381     507     54.5    10      37      99
St. Louis       61      775     622     55.9    9.5     35.89   105
Omaha   17      181     347     51.5    10.9    30.18   98
Albuquerque     15      46      244     56.8    8.9     7.77    58
Albany  56      44      116     47.6    8.8     33.36   135
Buffalo 11      391     463     47.1    12.4    36.11   166
Cincinnati      27      462     453     54      7.1     39.04   132
Cleveland       80      1007    751     49.7    10.9    34.99   155
Columbus        27      266     540     51.5    8.6     37.01   134
Philadelphia    79      1692    1950    54.6    9.6     39.93   115
Pittsburgh      63      347     520     50.4    9.4     36.22   147
Providence      136     343     179     50      10.6    42.75   125
Memphis 10      337     624     61.6    9.2     49.1    105
Nashville       23      275     448     59.4    7.9     46      119
Dallas  11      641     844     66.2    10.9    35.94   78
Houston 10      721     1233    68.9    10.8    48.19   103
Salt Lake City  28      137     176     51      8.7     15.17   89
Norfolk 38      96      308     59.3    10.6    44.68   116
Richmond        38      197     299     57.8    7.6     42.59   115
Seattle 40      379     531     51.1    9.4     38.79   164
Charleston      40      35      71      55.2    6.5     40.75   148
Milwaukee       20      569     717     45.7    11.8    29.07   123

Answer 1

Let's divide the data into those with wind speed < 10 and those with wind speed >= 10

Let be the mean SO2 level in the cities with wind speed < 10, and in those with wind speed >= 10

Let and be the respective std deviations of SO2 levels.

Hence, using the data given, we get: = 34.19, = 42.14, = 20.16, = 43.3

1) The hypothesis to run is (where and are respective true population means):

H₀: - = 0

H₁: - > 0

Hence, it is a One-sided t-test (since the population variance is not known, we cannot carry out a Z-test)

2) t-statistic = t = ( - )/ sqrt[(/n1) + (/n2)]

= -0.651

p-value = 0.2594

Hence, the p-value is too large, so we cannot reject the null hypothesis.

3) Conclusion: As explained above, We cannot conclude this is a reasonable expectation.