Question 1 The Great Northern Railway Company claims that its trains block a rai

Question

Question 1
The Great Northern Railway Company claims that its trains block a railway crossing in a rural community for no more than 12 minutes per train, on average. A local citizens group doubts this claim and measure the crossing times of a random selection of trains. The actual times (in minutes) that 16 randomly selected trains block the crossing were:
13.68 12.84 10.92 13.20 12.36 15.24 11.04 14.40
12.24 12.00 10.20 11.52 12.48 13.44 14.16 12.96
a) Test the claim at a significance level of 0.05 and assume that the crossing times are normally distributed. Clearly show the steps of the hypothesis test that you use, and express your final conclusion using a clear English sentence.
b) Why is it necessary to be told that the population of crossing times is normally distributed?
c) Calculate the 98% confidence interval for the mean crossing time for the trains.

Explanation / Answer

using minitab

Test of = 12 vs < 12

Variable N Mean StDev SE Mean 98% Upper Bound T P
times 16 12.668 1.360 0.340 13.432 1.96 0.966

here p value lessthan alpha, hence reject the null hypothesis

acccept alternative hypothesis, that means not morethan 12

98% value =2.2471

confindence intervel =lower bond=

12.668-2.2471*0.340

=11.9040

(11.9040,13.432 )

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