Question

Use the Tornadoes Data and your statistical expertise to answer the questions: Is it reasonable to claim that the number of tornadoes in January will affect the number of tornados in August?

1. What test/procedure did you perform?

• a. One-sided t-test
• b. Two-sided t-test
• c. Regression
• d. ​​Confidence interval

2. What is the relevant P-Value/margin of error?

• a. 1.7981E-05
• b. 8.17505E-06
• c. 4.08753E-06
• d. 0.05370006
• e. ​​None of these

3. Statistical Interpretation

• a. Since P-value is very small we are confident that the tornadoes in April will influence the tornadoes in August.
• b. Since P-value is not small we cannot claim that the tornadoes in April will influence the tornadoes in August.
• c. Since P-value is very small we are confident that the average numbers of tornados are different.
• d. ​​None of these.

4. Conclusion

• a. Yes, I am confident that the above assertion is reasonable.
• b. No, I cannot claim that the above assertion is reasonable.

Jan	Aug
7	13
2	27
12	16
14	24
2	49
3	33
2	42
17	20
11	46
16	38
9	48
1	27
12	51
15	26
14	79
21	61
1	58
39	28
5	66
3	70
9	55
19	50
33	59
33	51
24	107
52	60
12	38
5	82
23	65
16	126
5	73
2	64
18	34
13	76
1	47
2	108
0	67
6	63
17	61
14	36
11	60
29	46
15	115
17	112
13	120

Answer 1

Given that,
mean(x)=13.222
standard deviation , s.d1=10.954
number(n1)=45
y(mean)=57.711
standard deviation, s.d2 =27.99
number(n2)=45
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =2.015
since our test is two-tailed
reject Ho, if to < -2.015 OR if to > 2.015
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =13.222-57.711/sqrt((119.99012/45)+(783.4401/45))
to =-9.9291
| to | =9.9291
critical value
the value of |t α| with min (n1-1, n2-1) i.e 44 d.f is 2.015
we got |to| = 9.92914 & | t α | = 2.015
make decision
hence value of | to | > | t α| and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -9.9291 ) = 0
hence value of p0.05 > 0,here we reject Ho
ANSWERS
---------------
1.
option:B
two sided tailed
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: -9.9291
critical value: -2.015 , 2.015
decision: reject Ho
2.
p-value: 0
3.
option:C
c. Since P-value is very small we are confident that the average numbers of tornados are different.
4.
a. Yes, I am confident that the above assertion is reasonable.
we have enough evidence to support the claim that reasonable to claim that the number of tornadoes in January will affect the number of tornados in August.