Open Tornadoes-HW12 data. Is it reasonable to claim that the average annual numb
ID: 3053910 • Letter: O
Question
Open Tornadoes-HW12 data. Is it reasonable to claim that the average annual number of tornadoes occurred until 1970 (inclusive) was significantly different from the average annual number of tornadoes occurred after 1970? 6. What test/procedure did you perform? (5 points) a. One-sided t-test b. Two-sided t-test c. Regression d. Confidence Interval 7. What would be the correct Null-Hypothesis? (hint read end of lecture 24) (5 points) a. average annual number of tornadoes occurred until 1970 (inclusive) and average annual number of tornadoes occurred after 1970 are different. b. average annual number of tornadoes occurred until 1970 (inclusive) and average annual number of tornadoes occurred after 1970 are equal. c. average annual number of tornadoes occurred until 1970 (inclusive) and average annual number of tornadoes occurred after 1970 are related. d. average annual number of tornadoes occurred until 1970 (inclusive) and average annual number of tornadoes occurred after 1970 are not related. 8. What is the P-value/margin of error and what can be statistically concluded about the Null Hypothesis? (hint read end of lecture 24) (5 points) a. 4.19782 and we do not reject the Null Hypothesis b. 2.09891E-07 and we accept the Null Hypothesis c. 4.19782E-07 and we reject the Null Hypothesis d. 4.161353 and we accept the Null Hypothesis 9. What is the Statistical interpretation? (5 points) a. The P-value is much smaller than 5% thus we are very certain that the slope is not zero. b. The P-value is much smaller than 5% thus we are confident to say that the averages are significantly different. c. The P-value is greater than 5% thus we cannot claim that the averages are different. d. None of these. 10. What is the conclusion? (5 points) a. We are confident that the average annual number of tornadoes occurred until 1970 (inclusive) was significantly different from the average annual number of tornadoes occurred after 1970. b. We cannot be confident that the average annual number of tornadoes occurred until 1970 (inclusive) was significantly different from the average annual number of tornadoes occurred after 1970. c. The result is inconclusive thus we cannot conclude anything. d. None of these. DATA: Year Total Tornadoes 1950 213 1951 272 1952 252 1953 434 1954 562 1955 605 1956 516 1957 870 1958 576 1959 616 1960 628 1961 709 1962 669 1963 475 1964 716 1965 909 1966 597 1967 938 1968 672 1969 620 1970 666 1971 901 1972 753 1973 1114 1974 957 1975 931 1976 846 1977 864 1978 801 1979 867 1980 878 1981 794 1982 1059 1983 943 1984 919 1985 696 1986 777 1987 668 1988 714 1989 868 1990 1145 1991 1144 1992 1309 1993 1185 1994 1094
Explanation / Answer
R codes :
> tornadoes
[1] 213 272 252 434 562 605 516 870 576 616 628 709 669 475 716
[16] 909 597 938 672 620 666 901 753 1114 957 931 846 864 801 867
[31] 878 794 1059 943 919 696 777 668 714 868 1145 1144 1309 1185 1094
> year
[1] 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964
[16] 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979
[31] 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994
> before70=tornadoes[1:21]
> after70=tornadoes[22:45]
> before70
[1] 213 272 252 434 562 605 516 870 576 616 628 709 669 475 716 909 597 938 672
[20] 620 666
> after70
[1] 901 753 1114 957 931 846 864 801 867 878 794 1059 943 919 696
[16] 777 668 714 868 1145 1144 1309 1185 1094
> t.test(before70,after70)
Welch Two Sample t-test
data: before70 and after70
t = -6.0344, df = 40.08, p-value = 4.198e-07
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-440.7493 -219.5959
sample estimates:
mean of x mean of y
595.9524 926.1250
Solutions :
6. What test/procedure did you perform?
b. Two-sided t-test
7. What would be the correct Null-Hypothesis?
b. average annual number of tornadoes occurred until 1970 (inclusive) and average annual number of tornadoes occurred after 1970 are equal.
8. What is the P-value/margin of error and what can be statistically concluded about the Null Hypothesis?
c. 4.19782E-07 and we reject the Null Hypothesis
9. What is the Statistical interpretation?
b. The P-value is much smaller than 5% thus we are confident to say that the averages are significantly different.
10. What is the conclusion?
a. We are confident that the average annual number of tornadoes occurred until 1970 (inclusive) was significantly different from the average annual number of tornadoes occurred after 1970.
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