Answer to Question #116631 in Statistics and Probability for Muzzamil

Question

It is claimed that automobiles are driven on average more than 20,000 kilometers per year. To test this claim, 100 randomly selected automobile owners are asked to keep a record of the kilometers they travel. Would you agree with this claim if the random sample showed an average of 23,500 kilometers and a standard deviation of 3900 kilometers?

Answer 1

sample size n=100

sample mean x̄=23500

standard deviation σ=3900

the null hypothesis is:

H₀: μ = 20000

the alternative hypothesis is:

H₁: μ > 20000

z=(x̄-μ)/(σ/$\sqrt n$ )=(23500-20000)/(3900/10)=8.97

P(Z>8.97)=1-P(Z<8.97)=1-1=0

P-value is approximately 0, so we reject the null hypothesis and conclude that automobiles are driven on average more than 20,000 kilometers per year