Question

Two ride-sharing companies are competing for business in a large city. To help customers compare the companies, a data scientist selects a random sample of 40 completed rides from each of the two companies. From each sample, he computes the mean amount of time that passed between when the request for a pickup was placed and when the customer was picked up. Company A took, on average, 18 minutes to pick up customers with a standard deviation of 4 minutes. Company B took, on average, 12 minutes to pick up customers with a standard deviation of 10 minutes. (a) Construct and interpret a 98% confidence interval for the difference in mean response time for these two ride-sharing companies.

Answer 1

Given :

`$n_1 = n_2 = 40$`

`$\overline X_1 = 18$`

`$S_1 = 4$`

`$\overline X_2 = 12$`

`$S_2 =10$`

So we want to test :

`$H_0 : \mu_1=\mu_2 $` vs
`$H_1 : \mu_1 \\eq \mu_2 $`

a). For 98% confidence interval :

`$=\left((\overline X_1 - \overline X_2) \pm Tn_1+n_2-2, \alpha / 2 \sqrt{(s_1^2)/(n_1)+(s_2^2)/(n_2)}\right)$`

`$=\left((18-12) \pm 2.375 \sqrt{(4^2)/(40)+(10^2)/(40)}\right)$`

`$=(6 \pm 4.0445)$`

= (1.956, 10.045)