Question

My family bought a lovely suburban home that was advertised as having a 25 minute commute from UH. After a while I began to be suspicious that the commute was actually longer. I kept track of my commute times for 40 days and found my drive averaged 32 minutes with a standard deviation of 10 minutes. Does my evidence make their claim suspect? Find an answer with a 95% confidence interval. Find an answer using a hypothesis test with a Z score at the 99% level.

Answer 1

Formula for Confidence Interval for Population mean when population Standard deviation is not known

Confidence level : 95% = (100-95)/100 =0.05

/2 = 0.05/2 =0.025

n : Sample size: Number of commute days = 40

: Sample mean : Sample average commute time =32

s: Sample standard deviation = 10

Claim : Average Commute time > 25 minutes; > 25

t_/2,n-1 =t_0.025,39 = 2.0227

95% confidence interval

As 25 is greater than the lower confidence limit;

There is sufficient evidence to conclude that the average commute time is >25 .

Your evidence makes their claim suspect.

Null hypothesis : H_o:  =25

Alternate hypothesis : H_a : > 25

Right tailed test

for 99% confidence level = (100-99)/100 =0.01

As P-Value i.e. is less than Level of significance i.e (P-value:0 < 0.01:Level of significance); Reject Null Hypothesis

There is sufficient evidence to conclude that the average commute time is >25 .

Your evidence makes their claim suspect.