Nathan and Mohit are friends who live on opposite sides of the country. During quarantine, they...

Nathan and Mohit are friends who live on opposite sides of the country. During quarantine, they have decided to compare the number of cars that pass by their houses per day. Over the last 30 days, Nathan sees an average of 6.2 cars pass by, with a standard deviation of 1.4. Mohit started a bit before Nathan, and over the last 40 days, he’s seen an average of 7.4 cars with a standard deviation of 1.9. The degrees of freedom for this problem is df = 5.

a) Is this an observational study or an experiment?

b) Is it appropriate to assume the difference in Nathan and Mohit’s means is approximately normally distributed?

c) Construct a 95% confidence interval for difference in number of cars Nathan and Mohit see.

d) Mohit wonders if there is enough evidence to say that he and Nathan see a different number of cars per day. Test this at α = .05. What are the hypotheses for an appropriate test?

e) Calculate the t-test statistic for the test defined in part (c).

f) Find the P-value for the test.

g) Make your conclusion for the hypothesis test and interpret its meaning in the context of the problem.

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