Question

A meteorologist who sampled 35 randomly selected thunderstorms found that they had a mean speed of travel across a state of 16 miles per hour and a standard deviation of 1.5 miles per hour

find a 98% confidence interval for the population mean travel speed for the thunderstorms across a state ( round to 1 decimal place)

Find the margin of error ( round to 1 decimal place)

if the meteorologist wants her estimate to be within 0.3 with 98% confidence, what is the sample size required ? the answer has to be a whole number

Answer 1

sample mean, xbar = 16
sample standard deviation, s = 1.5
sample size, n = 35
degrees of freedom, df = n - 1 = 34

Given CI level is 98%, hence α = 1 - 0.98 = 0.02
α/2 = 0.02/2 = 0.01, tc = t(α/2, df) = 2.441

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (16 - 2.441 * 1.5/sqrt(35) , 16 + 2.441 * 1.5/sqrt(35))
CI = (15.4 , 16.6)

ME = tc * s/sqrt(n)
ME = 2.441 * 1.5/sqrt(35)
ME = 0.6

The following information is provided,
Significance Level, α = 0.02, Margin or Error, E = 0.3, s = 1.5

The critical value for significance level, α = 0.02 is 2.441

The following formula is used to compute the minimum sample size required to estimate the population mean μ within the required margin of error:
n >= (tc *s/E)^2
n = (2.441 * 1.5/0.3)^2
n = 148.96

Therefore, the sample size needed to satisfy the condition n >= 148.96 and it must be an integer number, we conclude that the minimum required sample size is n = 149
Ans : Sample size, n = 149