Question

State University offers several sections of a Business Statistics course in an in-class and online format. Both formats are administered the same final exam each year. You have been assigned to test the hypothesis that the average final exam score of in-class students is different from the average final exam score of online students. The following data summarizes the sample statistics for the final exam scores for students from each format. Assume that the population variances are unequal. In-class Format Online Format Sample mean 86.5 84.7 Sample size 22 25 Sample standard deviation 4.6 6.1 If Population 1 is defined as in-class format and Population 2 is defined as online format, and using LaTeX: \alpha α = 0.05, the conclusion for this hypothesis test would be because the absolute value of the test statistic is ______________________________________________________________. less than the absolute value of the critical value, you can conclude that the average final exam score of in-class students is equal to the average final exam score of online students less than the absolute value of the critical value, you cannot conclude that the average final exam score of in-class students is different from the average final exam score of online students more than the absolute value of the critical value, you cannot conclude that the average final exam score of in-class students is different from the average final exam score of online students more than the absolute value of the critical value, you can conclude that the average final exam score of in-class students is different from the average final exam score of online students

Answer 1

We have to test the hypothesis that the average final exam score of in-class students is different from the average final exam score of online students.

So, Null hypothesis will be that there is no difference between the two mean values and alternate hypothesis will be the given statement

It is given that

We have to find the test statistics value.

We know that we have two different populations, i.e. in class and online class with unequal variances. So, t test would be apropriate to use in this case.

Formula for the t test statistics is given as

setting the given values, we get

on solving, we get

t test statistics = 1.1499 (rounded to 4 decimal) or 1.150(rounded to 3 decimal) or 1.15(rounded to 2 decimal)

Please choose t test statistics value according to the required decimal places. Decimal places are not asked in question, So you can use 2 decimal places

t statistics = 1.15

we know that degree of freedom is minimum of (n1-1) or (n2-1)

n1-1 = 22-1 = 21

n2-1 = 25-1 = 24

So, 21 is less than 24

Thus, degree of freedom = 21

t critical value using df = 21 and two tailed hypothesis, using the t critical table, we get

t critical =

So, we will reject the null hypothesis if t calculated value is less than -2.08 or greater than +2.08

Now, using degree of freedom 21 and t value of 1.15 in the t distribution table, we get

p value = 0.2631

So, p value is greater than significance level of 0.05, fail to reject the null hypotheis

Thus, we can conclude that the average final exam score of in-class students is different from the average final exam score of online students.

Statement D is correct

you can conclude that the average final exam score of in-class students is different from the average final exam score of online students

t calculated value is between the t critical values