Arthur believes that people who play Pokemon Go, on average, take a different nu

Question

Arthur believes that people who play Pokemon Go, on average, take a different number steps per day than people who don't play it. To test his hypothesis, he gives 100 people pedometers and records their data for one day. Forty-six of these people are regular players of Pokemon Go, and they averaged 8, 492.15 steps per day. The remaining participants averaged 7, 830.69 steps per day. Assuming equal population variances in the two groups, the pooled estimate of the standard error for the difference in mean number of steps between these two groups is = 247.09 steps. Find the 95% confidence interval for the difference in mean number of steps of Pokemon Go players vs. non-players. Based on your answer in part (a), did the two groups' steps significantly differ, on average? How do you know? Conduct a hypothesis test to show that your answer in part (b) is correct. Assume your assumptions have been met.

Explanation / Answer

a) here estimate difference =X1-X2=8492.15-7830.69=661.46

std error =247.09

for 95% CI, z=1.96

hence 95% Confidence interval =mean differnce +/-z*std error =177.1725 ; 1145.748

b) Yes ; as our confidence interval does not contain 0 as possible value

c) from here test stat z =(X1-X2)/std error =2.677

for 0.05 level of significance critical value of z =+/-1.96

as test stat falls in rejection region; hence we reject null hypothesis, and conclude that there is significant differnece

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