Question

Tornado Length (in miles)

1.15
8.98
2.47
1.15
0.49
3.38
5.07
0.49
1.3
2.15
0.94
1.8
1.9
6.69
3.49
7.69
0.17
0.11
0.11
0.11
0.49
4.42
0.55
21.46
23.01
2.09
0.2
7.05
14.92
14.2
1.03
3.9
6.56
4.28
5.8
1.19
10.49
2
9.49
8.34
2.46
5.51
7.82
5.99
0.68
8.26
0.86
1.78
0.21
0.11
0.73
0.26
0.72
1.61
3.53
8.7
0.38
0.11
0.41
0.1
0.11
0.63
2.08
5.72
1.04
0.36
0.53
0.5
0.11
4.82
2.41
1.19
5.47
0.47
1.09
0.49
0.95
0.19
1.15
3.43
5.01
1.73
3.43
0.11
0.11

d) Use statistical software to construct a 95​% confidence interval for the mean tornado length. Select the correct choice below and fill in the answer boxes to complete your choice.

​(Use ascending order. Round to two decimal places as​ needed.)

A.There is 95​% probability that the true mean length of a tornado is between _____ miles and _____ miles.

B.We are 95​% confident that the population mean length of a tornado is between _____ miles and _____ miles.

C.If repeated samples are​ taken, 95​% of them will have a sample mean between ____ miles and ______ miles.

Answer 1

We will use R software . All the codes are marked in BOLD

# Computing 95% confidence interval
# Importing data from Excel
n <- length(q1$`Tornado Length (in miles)`) # number of observations
x_bar <- mean(q1$`Tornado Length (in miles)`) # Sample mean
s <- sd(q1$`Tornado Length (in miles)`) # sample standard deviation
t <- abs(qt(0.5*(1-0.95), n-1, lower.tail = TRUE))
lcl <- x_bar-(t*s)/sqrt(n) # lower confidence limit
ucl <- x_bar+(t*s)/sqrt(n) # upper confidence limit
print(n)
print(x_bar)
print(s)
print(t)
print(round(lcl,2))
print(round(ucl,2))

Hence , the confidence limit is 2.4 miles < Tornado Length < 4.3

Therefore, the correct option is (A)

A.There is 95​% probability that the true mean length of a tornado is between 2.4 miles and 4.3 miles.