Question

A meteorologist who sampled 7 thunderstorms found that the average speed at which they traveled across a certain state was 16 miles per hour. The standard deviation of the sample was 4.3 miles per hour. Round the final answers to at least two decimal places.

Find the 80% confidence interval of the mean. Assume the variable is normally distributed.

Answer 1

Solution :

Given that,

= 16

s =4.3

n = 7

Degrees of freedom = df = n - 1 =7 - 1 = 6

a ) At 80% confidence level the t is ,

= 1 - 80% = 1 - 0.80 = 0.20

  / 2= 0.20 / 2 = 0.10

t /2,df = t0.10,6 = 1.440 ( using student t table)

Margin of error = E = t/2,df * (s /n)

= 1.440 * (4.3 / 7)

= 2.34

The 80% confidence interval is,

- E < < + E

16 - 2.34 < <16 + 2.34

13.66 < < 18.34