Question

Suppose a student organization at a university collected data for a study involving class sizes from different departments. The following table shows the average class size from a random sample of classes in the business school vs. the average class size from a random sample of classes in the engineering school. Data for the sample sizes and standard deviations are also shown. Use this data to complete parts a through c.

	Business	Engineering
Sample mean	38.5

31.2

Sample standard deviation	10.6

12.5

Sample size	11

15

a. Perform a hypothesis test using alpha=0.01

to determine if the average class size differs between these departments. Assume the population variances for the number of students per class are not equal.

Determine the null and alternative hypotheses for the test.

Upper H 0 : mu 1 minus mu 2

▼

greater than

equals

greater than or equals

less than or equals

less than

not equals

0

Upper H 1 : mu 1 minus mu 2

▼

greater than or equals

less than

equals

not equals

less than or equals

greater than

0

Calculate the appropriate test statistic and interpret the result.

The test statistic is

nothing

.

​(Round to two decimal places as​ needed.)

The critical​ value(s) is(are)

nothing

.

​(Round to two decimal places as needed. Use a comma to separate answers as​ needed.)

Because the test statistic

▼

does not fall within the critical values,

is less than the critical value,

is greater than the critical value,

falls within the critical values,

▼

do not reject

reject

the null hypothesis. The average business class size is

▼

not different from

different from

the average engineering class size.

b. Identify the​ p-value from part a and interpret the result.

The​ p-value is

nothing

.

​(Round to three decimal places as​ needed.)

Interpret the result. Choose the correct answer below.

A.

Since the​ p-value is

equal to or greater

than the significance​ level,

do not reject

the null hypothesis.

B.

Since the​ p-value is

equal to or greater

than the significance​ level,

reject

the null hypothesis.

C.

Since the​ p-value is

less

than the significance​ level,

reject

the null hypothesis.

D.

Since the​ p-value is

less

than the significance​ level,

do not reject

the null hypothesis.

. What assumptions need to be made in order to perform this​ procedure?

A.

If both sample sizes are not each at least​ 30, then one must assume that the underlying populations are normally distributed to perform this procedure.​ Also, one must assume that the samples are independent.

B.

Since the sample sizes are large​ enough, no assumptions are needed.

C.

Although the sample size in the second sample is large​ enough, it must be assumed that the distribution for the first sample is normally distributed.

D.

Although the sample size in the first sample is large​ enough, it must be assumed that the distribution for the second sample is normally distributed.

Answer 1

Using t test for independent samples population variances unequal