Answer to Question #230445 in Statistics and Probability for JPA

Question

The following are independent random samples of the IQ of teenagers belonging to two different groups . Use the level of significance @0.05 = 2.101 to test the claim that teenagers of Group A have lower average IQ than teenagers of Group B.

Group A = 88, 94, 91, 95, 101, 98, 96, 105, 95, 85

Group B = 95, 85, 93, 97, 103, 107, 90, 114, 85, 78

Answer 1

$H_0: \mu_A=\mu_B \\ H_1: \mu_A<\mu_B$

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 = 0.07611) suggests that we should not reject the H0 (variances are not different). Therefore, we should conduct a t-test.

Since $P_{cal}=0.51 > P = 0.05$

Accept H₀.

There is enough evidence to conclude that teenagers of Group A do not have lower average IQ than teenagers of Group B. (5% level of significance).