Researchers investigated whether instructor ratings posted on a website (WEB) ar

Question

Researchers investigated whether instructor ratings posted on a website (WEB) are cormelated with the formal in-class student evaluations of teaching (SET) hat all universities are required to administer at the end of the semester. Data colected for n semester. Data collected for n 418 university instructors yielded a correlation between WEB and SET ratings of 0.59 Complete parts a through e below a Give the equation of a linear model relating SET rating ) to WEB rating (x). Choose the coect answer below b Give a practical interpretation of the value r-0.59.Choose the cormrect anewer below and, if necessary, il in the answer bex to complete your choice OA. AboutIi%ofthe sample variation in WEB ratng can be explined by usingthe SET ratng in the inear model Round to the nearest percent as needed) O B. The SET rating tends to decrease as the WEB ating increases for the given sample O e. Abouti.. % of he sarple vanaton in SET rating can be e-planed by using the WEB rat ng nthsaneJm0del. Round to the nearest percent as needed) O D. The SET rating tends to increase as the WED rating increases for the given sample e is the estimated slope of the line, part a, postive or negative? Explain OA. The estimated slope is negative because the value of r is posve OC. The estimated slope is pesive because the ooefficient of determination is positive O D. The estimated slope is postive because the value of n is posive O E. More information regarding the linear model is necessary to determine the drection of the sope d. A test of the null hypothesis Ho p0 yekded a p-value of 0.006 Interpret this result with an alpha level of 0.01 'ine na hypotes" There ?: sumoent evdenoe to claim that lhe popaton correlaton ooencert's not 1

Explanation / Answer

Solution :

Given that, n= 418 and correlation coefficient between WEB and SET is 0.59.Dependent variable SET is y and WEB is independnet variable x.

a)The correct option is D. As here we have only one independent variable, the linear model is,

E(y ) =bo+b1x

b) The correct option is D.

The SET rating tends to increase as the WEB rating increase for sample.

c) The correct option is B.

The estimated slope is positive because the value of r is positive.

d) Given that alpha =0.01 and p-value = 0.006

As alpha(0.01) > p-value (0.006) we reject Ho.Conclusion is,

Reject the null hypothesis .There is sufficient evidence to claim that the popuation correlation coefficient is not 0.06

e.coefficient of determination r2 =0.59*0.59 =0.3481

Interpretation:About 34.81% of the sample variation in SET rating is explained by using the WEB rating in the linear model.

As the

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