Answer to Question #218107 in Statistics and Probability for Ash

Question

To compare the price of a certain product in two cities, ten shops were selected random in each city. The following observations were obtained: 

City A: 61 63 56 63 56 62 59 60 61 65

City B: 55 54 47 59 51 61 57 54 64 58 

Test whether the average price can be said to be the same in the two cities (5% level of significance). 

Answer 1

$H_0: \mu_1=\mu_2 \\ H_1: \mu_1≠ \mu_2$

Using R

Let’s test date for normality using shapiro.test(). Since these two samples are independent we need to test them individually. Here are just the p-values from the normality test.

The samples appear to be normally distributed so we may proceed with a standard t-test. The t-test also assumes that the variances are equal.

Let’s test that, too, using the var.test( ) variance test.

The resulting p-value (p = 0.1437) suggests that we should not reject the H₀ (variances are not different). Therefore, we should conduct a t-test.

Since P_{cal}=0.02075 < P = 0.05

Reject H₀.

There is enough evidence to conclude that the average price can NOT be said to be the same in the two cities (5% level of significance).