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

Solution :

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 $H_1 : \mu_1 \neq \mu_2$

a). For 98% confidence interval :

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

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

$=(6 \pm 4.0445)$

= (1.956, 10.045)