University College is concerned that out of state students m

University College is concerned that out of state students may be receiving lower grades than other students. Two independent random samples have been selected: 165 observations from population 1 (Out of state students) and 177 from population 2 (University College students). The sample means obtained are X1(bar)=86 and X2(bar)=87. It is known from previous studies that the population variances are 8.1 and 7.3 respectively. Using a level of significance of .01, is there evidence that the out of state students may be receiving lower grades? Fully explain your answer.

Solution

To Test

Ho : ?1= ?2 Vs H1 : ?1< ?2 (one tailed test)

Test Statistics: (As n is large >30, so we use Normal Test)

t-value= -3.3332

degress of freedom=340

The P-Value is 0.000477

Since the P-value 0.000477 < 0.1, we reject H0. It is statistically significant.

At the 10% level of significance, the data provides enough evidence to reject the null hypothesis. Thus we conclude at 0.1 level of significance that the out of students are receiving lower grades .