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: Is it reasonable to claim that cities with precipitation of less than 100 days have average temperature of less than 65 degrees F? Given the data your job is to confirm or disprove this claim.

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 claim.
• b. No, we cannot confirm that this is a reasonable claim.

  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

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: Is it reasonable to claim that cities with precipitation of less than 100 days have average temperature of less than 65 degrees F? Given the data your job is to confirm or disprove this claim.

I. What test/procedure did you perform? (6.66 points)

Answer: 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.

Answer: 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)

Answer: a. Yes, this is a reasonable claim.

b. No, we cannot confirm that this is a reasonable claim.

precipitation of less than 100 days = 9 cities

CITY	SO2	MANUF	POP	TEMP	WIND	PRECIP-INCHES	PRECIP-#DAYS
Phoenix	11	213	582	70.3	6	7.05	36
Albuquerque	15	46	244	56.8	8.9	7.77	58
SanFrancisco	16	453	716	56.7	8.7	20.66	67
Dallas	11	641	844	66.2	10.9	35.94	78
Wichita	10	125	277	56.6	12.7	30.58	82
Denver	24	454	515	51.9	9	12.95	86
SaltLakeCity	28	137	176	51	8.7	15.17	89
Omaha	17	181	347	51.5	10.9	30.18	98
KansasCity	18	381	507	54.5	10	37	99

t Test for Hypothesis of the Mean
Data
Null Hypothesis                m=	65
Level of Significance	0.05
Sample Size	9
Sample Mean	57.2778
Sample Standard Deviation	6.7048
Intermediate Calculations
Standard Error of the Mean	2.2349
Degrees of Freedom	8
t Test Statistic	-3.4552
Lower-Tail Test
Lower Critical Value	-1.8595
p-Value	0.0043
Reject the null hypothesis

Calculated t= -3.4552, P=0.0043 which is < 0.05 level of significance. Ho is rejected.

There is enough evidence to support the claim that cities with precipitation of less than 100 days have average temperature of less than 65 degrees F.