Question

1. The University is interested in determining if the number of people coming to work by pedal bicycle has changed from 2016 to 2017. Over the course of a week (Mon-Sun) they count the number of cyclists who enter campus at the North campus cycle path entrance between 8am-10am each day. The University have data from the same week in 2016. The counts for each day of the week for 2016 and 2017 are given in Table:

   	Mon	Tues	Wed	Thurs	Fri	Sat	Sun
   2016	243	175	255	187	241	53	32
   2017	254	242	250	263	235	51	35

   1. Describe one positive and one negative aspect of the University's sampling strategy
   2. Explain why a paired approach is appropriate for this test
   3. Write down appropriate null and alternative hypotheses for this test.
   4. Calculate the mean and variance of the differences di=xi-yi.
   5. What assumptions are required to conduct your hypothesis test from (c), does this data satisfy them?
   6. Using your answer to part (d), or otherwise, calculate a 90% confidence interval for the difference in the average number of cyclists.
   7. Using your answer to part (f), or otherwise, test your hypothesis from (c)  at the 10% level. You should clearly state the conclusion of your test.
   8. From Table 1 it looks like Tuesday and Thursday have the largest difference from one year to the next.  Why is it wrong to now testing the hypothesis  “2017 has more cyclists on Tuesdays and Thursdays than in 2016”?

Please explain part h) more details, thanks a lot.

Answer 1

a) here the positive aspect of university's samolsam strategy is that they have collected paired data.

Negative strategy is that they have collected data between 8-10 am only and for one week only .

b) As University is interested in determining if the number of people coming to work by pedal bicycle has changed from 2016 to 2017 that's why paired approach is appropriate.

c) H0: mean difference di is zero

H1: mean difference di is not zero

d)

Tell me what you want to do... Page Layout Formulas Data File Home Insert Review View Team f D16 A B C D F G H K M di-xi-yi Xi 1 2 Mon t-Test: Paired Two Sample for Means 243 254 -11 3 Tue 175 242 67 4 Wed 255 250 Varigble 1 Variable 2 5 Thur 187 263 -76 Mean 169.4285714 190 6 Fri 241 235 8439.952381 10183.33333 6 Variance 7 Sat Observations 53 51 2 7 7 8 Sun Pearson Correlation 35 32 3 0.937014931 Hypothesized Mean Difference 0 10 mean di df 6 -20.5714 var di 1249.619 11 t Stat -1.539659386 P(T<-t) one-tail 12 0.087284969 t Critical one-tail 13 1.943180281 P(T<-t) two-tail 0.174569937 14 Critical two-tail 2.446911851 15 16 17 18 19