Use the Tornadoes Data and your statistical expertise to answer the questions: Is it reasonable to claim that the averag...
Use the Tornadoes Data and your statistical expertise to answer the questions: Is it reasonable to claim that the average number of observed tornadoes per year is different from the average number of tornado related deaths per year?
5. What test/procedure did you perform?
- a. One-sided t-test
- b. Two-sided t-test
- c. Regression
- d. Confidence interval
6. What is the P-Value/margin of error?
- a. 0.007034504
- b. 0.34922
- c. 4.07497E-24
- d. 2.03749E-24
- e. None of these
7. Statistical Interpretation
- a. Since P-value is very small we are confident that the number of tornadoes will influence the tornadoes' deaths.
- b. Since P-value is not small we cannot claim that the number of tornadoes will influence the tornadoes' deaths.
- c. Since P-value is very small we are confident that the averages of these two data are different.
- d. None of these.
8. Conclusion
- a. Yes, I am confident that the above assertion is correct.
- b. No, I cannot claim that the above assertion is correct.
Tornadoes and Deaths by Year and Month (1950-1994)
Year Total Tornadoes Tornadoes by Month Total Deaths Deaths by Month
Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec
1950 201 7 20 21 15 61 28 23 13 3 2 4 4 70 1 45 1 12 2 6 0 0 0 0 0 3
1951 260 2 10 6 26 57 76 23 27 9 2 12 10 34 0 1 0 2 7 9 5 0 8 0 1 1
1952 240 12 27 43 37 34 34 27 16 1 0 6 3 230 0 10 209 4 2 2 2 1 0 0 0 0
1953 422 14 16 40 47 94 111 32 24 5 6 12 21 519 0 3 24 36 163 244 0 0 0 0 0 49
1954 550 2 17 62 113 101 107 45 49 21 14 2 17 36 0 2 10 2 9 5 0 1 3 2 0 2
1955 593 3 4 43 99 148 153 49 33 15 23 20 3 129 0 0 5 7 106 2 5 0 2 1 1 0
1956 504 2 47 31 85 79 65 92 42 16 29 7 9 83 0 8 1 67 4 0 1 2 0 0 0 0
1957 858 17 5 38 216 228 147 55 20 17 18 59 38 193 13 0 1 30 87 14 0 0 2 2 25 19
1958 564 11 20 15 76 68 128 121 46 24 9 45 1 67 0 13 0 4 0 43 1 1 1 4 0 0
1959 604 16 20 43 30 226 73 63 38 58 24 11 2 58 3 21 9 1 8 2 0 0 14 0 0 0
1960 616 9 28 28 70 201 125 42 48 21 18 25 1 46 0 0 0 7 34 3 0 1 0 1 0 0
1961 697 1 31 124 74 137 107 77 27 53 14 36 16 52 0 0 7 4 23 2 0 0 15 0 1 0
1962 657 12 25 37 41 200 171 78 51 24 11 5 2 30 1 0 17 2 4 0 0 6 0 0 0 0
1963 463 15 6 48 84 71 90 62 26 33 13 15 0 31 1 0 8 16 1 0 0 2 3 0 0 0
1964 704 14 2 36 157 134 137 63 79 25 22 17 18 73 10 0 6 15 16 0 0 2 0 22 0 2
1965 897 21 32 34 123 273 147 85 61 64 16 34 7 301 0 0 2 268 17 7 0 1 0 1 5 0
1966 585 1 28 12 80 98 126 100 58 22 29 20 11 98 0 0 58 12 0 19 3 0 0 6 0 0
1967 926 39 8 42 149 116 210 90 28 139 36 8 61 114 7 0 3 73 3 6 1 2 5 4 0 10
1968 660 5 7 28 102 145 136 56 66 25 14 44 32 131 0 0 0 40 72 11 2 2 0 0 3 1
1969 608 3 5 8 68 145 137 98 70 20 26 5 23 66 32 0 1 2 4 7 0 19 0 0 0 1
1970 654 9 16 25 117 88 134 82 55 54 50 10 14 73 0 0 2 30 26 6 3 0 0 6 0 0
1971 889 19 83 40 75 166 199 100 50 47 38 16 56 159 1 134 2 11 7 1 1 0 0 0 0 2
1972 741 33 7 69 96 140 114 115 59 49 34 17 8 27 5 0 0 16 0 2 0 2 0 0 2 0
1973 1102 33 10 80 150 250 224 80 51 69 25 81 49 89 1 0 17 10 35 3 1 4 3 0 12 3
1974 945 24 23 36 267 144 194 59 107 25 45 13 8 366 2 0 1 317 10 31 0 0 0 5 0 0
1975 919 52 45 84 108 188 196 79 60 34 12 39 22 60 12 7 12 13 5 6 2 2 0 0 0 1
1976 834 12 36 180 113 155 169 84 38 35 11 0 1 44 0 5 21 1 8 3 2 1 3 0 0 0
1977 852 5 17 64 88 228 132 99 82 65 25 24 23 43 0 2 0 26 4 0 1 6 1 1 0 2
1978 789 23 7 17 107 213 148 143 65 20 7 9 30 53 2 0 0 4 7 17 11 1 6 0 0 5
1979 855 16 4 53 123 112 150 132 126 69 47 21 2 84 0 0 1 58 2 8 1 5 2 7 0 0
1980 866 5 11 41 137 203 217 95 73 37 43 3 1 28 0 0 2 4 8 7 5 0 1 1 0 0
1981 782 2 25 33 84 187 223 98 64 26 32 7 1 24 0 2 1 13 0 8 0 0 0 0 0 0
1982 1047 18 3 60 150 329 196 95 34 38 9 19 96 64 1 0 6 30 14 4 0 0 2 0 0 7
1983 931 13 41 71 65 249 178 99 76 19 13 49 58 34 2 1 0 6 14 2 4 0 0 0 0 5
1984 907 1 27 73 176 169 242 72 47 17 49 30 4 122 0 0 64 33 6 14 0 0 0 4 1 0
1985 684 2 7 38 134 182 82 51 108 40 18 19 3 94 0 0 2 5 78 3 0 3 0 0 3 0
1986 765 0 30 76 84 173 134 88 67 65 26 17 5 15 0 2 6 2 1 0 3 1 0 0 0 0
1987 656 6 19 38 20 126 132 163 63 19 1 55 14 59 0 6 1 1 31 2 0 1 0 0 11 6
1988 702 17 4 28 58 132 63 103 61 76 19 121 20 32 5 0 1 4 3 0 0 3 1 0 14 1
1989 856 14 18 43 82 231 252 59 36 31 30 57 3 50 0 0 1 0 9 5 0 0 0 4 31 0
1990 1133 11 57 86 108 243 329 106 60 45 35 18 35 53 0 1 3 0 5 11 0 29 0 2 0 2
1991 1132 29 11 157 204 335 216 64 46 26 21 20 3 39 1 0 13 21 0 1 1 0 0 0 2 0
1992 1297 15 29 55 53 137 399 213 115 81 34 146 20 39 0 0 5 0 0 1 0 3 0 4 26 0
1993 1173 17 34 48 85 177 313 242 112 65 55 19 6 33 0 3 5 10 2 1 0 6 2 4 0 0
1994 1082 13 9 58 205 161 234 155 120 30 51 42 4 69 0 0 40 12 0 3 3 4 0 0 7 0Homework Answers
We will use the following data:
| Year | Total tornadoes | Deaths |
| 1950 | 201 | 70 |
| 1951 | 260 | 34 |
| 1952 | 240 | 230 |
| 1953 | 422 | 519 |
| 1954 | 550 | 36 |
| 1955 | 593 | 129 |
| 1956 | 504 | 83 |
| 1957 | 858 | 193 |
| 1958 | 564 | 67 |
| 1959 | 604 | 58 |
| 1960 | 616 | 46 |
| 1961 | 697 | 52 |
| 1962 | 657 | 30 |
| 1963 | 463 | 31 |
| 1964 | 704 | 73 |
| 1965 | 897 | 301 |
| 1966 | 585 | 98 |
| 1967 | 926 | 114 |
| 1968 | 660 | 131 |
| 1969 | 608 | 66 |
| 1970 | 654 | 73 |
| 1971 | 889 | 159 |
| 1972 | 741 | 27 |
| 1973 | 1102 | 89 |
| 1974 | 945 | 366 |
| 1975 | 919 | 60 |
| 1976 | 834 | 44 |
| 1977 | 852 | 43 |
| 1978 | 789 | 53 |
| 1979 | 855 | 84 |
| 1980 | 866 | 28 |
| 1981 | 782 | 24 |
| 1982 | 1047 | 64 |
| 1983 | 931 | 34 |
| 1984 | 907 | 122 |
| 1985 | 684 | 94 |
| 1986 | 765 | 15 |
| 1987 | 656 | 59 |
| 1988 | 702 | 32 |
| 1989 | 856 | 50 |
| 1990 | 1133 | 53 |
| 1991 | 1132 | 39 |
| 1992 | 1297 | 39 |
| 1993 | 1173 | 33 |
| 1994 | 1082 | 69 |
We will use the regression test to see that if these two variables are related to each other and their relationship. The independent variable here is Number of tornadoes and dependent variable is tornadoes related deaths
5. C) Regression
6. We can perform regression in Excel or SPSS to find the results.
In Excel, Go to Data -> Data analysis -> Regression -> Select the data
The results are:
| SUMMARY OUTPUT | ||||||||
| Regression Statistics | ||||||||
| Multiple R | 0.142848 | |||||||
| R Square | 0.020406 | |||||||
| Adjusted R Square | -0.00238 | |||||||
| Standard Error | 96.47912 | |||||||
| Observations | 45 | |||||||
| ANOVA | ||||||||
| df | SS | MS | F | Significance F | ||||
| Regression | 1 | 8337.507 | 8337.507 | 0.895714 | 0.349222 | |||
| Residual | 43 | 400253.5 | 9308.22 | |||||
| Total | 44 | 408591 | ||||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
| Intercept | 134.163 | 47.3953 | 2.830725 | 0.007035 | 38.58132 | 229.7448 | 38.58132 | 229.7448 |
| Tornadoes | -0.05623 | 0.059418 | -0.94642 | 0.349222 | -0.17606 | 0.063593 | -0.17606 | 0.063593 |
The p-value = 0.34922
6. What is the P-Value/margin of error?
B) 0.34922 is correct
7. Statistical Interpretation
As the p-value > 0.05, we cannot reject the null hypothesis.
Correct option: B). Since P-value is not small we cannot claim that the number of tornadoes will influence the tornadoes' deaths.
8. Correct option: B). No, I cannot claim that the above assertion is correct.
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Titration #3
mL base added
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mL base added
pH
mL base added
pH
1
0.7
1
0.7
1
0.7
2
1.1
2
1
2
0.9
3
1.5
3
1.4
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1.3
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1.7
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1.6
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1.5
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5
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20
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6
17
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3
0
7
15
14
23
M
3
20
5
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pH
1
0.7
1
0.7
1
0.7
2
1.1
2
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3
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