Question

Do faculty and students have similar perceptions of what types of behavior are inappropriate in the classroom? This question was examined by the author of an article. Each individual in a random sample of 173 students in general education classes at a large public university was asked to judge various behaviors on a scale from 1 (totally inappropriate) to 5 (totally appropriate). Individuals in a random sample of 98 faculty members also rated the same behaviors.

The mean rating for three of the behaviors studied are shown here (the means are consistent with data provided by the author of the article). The sample standard deviations were not given, but for purposes of this exercise, assume that they are all equal to 1.0.

Student Behavior	Student Mean Rating	Faculty Mean Rating
Wearing hats in the classroom	2.84	3.62
Addressing instructor by first name	2.92	2.12
Talking on a cell phone	1.10	1.08

(a)

Is there sufficient evidence to conclude that the mean "appropriateness" score assigned to wearing a hat in class differs for students and faculty? (Use α = 0.05. Use a statistical computer package to calculate the P-value. Use μ_Students − μ_Faculty. Round your test statistic to two decimal places, your df down to the nearest whole number, and your P-value to three decimal places.)

t=

df=

P-value=

State your conclusion.

We do not reject H₀. We do not have convincing evidence that the mean appropriateness score assigned to wearing a hat in class differs for students and faculty.

We reject H₀. We do not have convincing evidence that the mean appropriateness score assigned to wearing a hat in class differs for students and faculty.    

We reject H₀. We have convincing evidence that the mean appropriateness score assigned to wearing a hat in class differs for students and faculty.

We do not reject H₀. We have convincing evidence that the mean appropriateness score assigned to wearing a hat in class differs for students and faculty.

(b)

Is there sufficient evidence to conclude that the mean "appropriateness" score assigned to addressing an instructor by his or her first name is greater for students than for faculty? (Use α = 0.05. Use a statistical computer package to calculate the P-value. Use μ_Students − μ_Faculty. Round your test statistic to two decimal places, your df down to the nearest whole number, and your P-value to three decimal places.)

t=

df=

P-value=

State your conclusion.

We do not reject H₀. We do not have convincing evidence that the mean appropriateness score assigned to addressing an instructor by their first name is greater for students than for faculty.

We reject H₀. We have convincing evidence that the mean appropriateness score assigned to addressing an instructor by their first name is greater for students than for faculty.   

We reject H₀. We do not have convincing evidence that the mean appropriateness score assigned to addressing an instructor by their first name is greater for students than for faculty.

We do not reject H₀. We have convincing evidence that the mean appropriateness score assigned to addressing an instructor by their first name is greater for students than for faculty.

(c)

Is there sufficient evidence to conclude that the mean "appropriateness" score assigned to talking on a cell phone differs for students and faculty? (Use α = 0.05. Use a statistical computer package to calculate the P-value. Use μ_Students − μ_Faculty. Round your test statistic to two decimal places, your df down to the nearest whole number, and your P-value to three decimal places.)

t=

df=

P-value=

State your conclusion.

We do not reject H₀. We have convincing evidence that the mean appropriateness score assigned to talking on a cell phone in class differs for students and faculty.

We reject H₀. We have convincing evidence that the mean appropriateness score assigned to talking on a cell phone in class differs for students and faculty.    

We do not reject H₀. We do not have convincing evidence that the mean appropriateness score assigned to talking on a cell phone in class differs for students and faculty.

We reject H₀. We do not have convincing evidence that the mean appropriateness score assigned to talking on a cell phone in class differs for students and faculty.

(d)

Does the result of the test in part (c) imply that students and faculty consider it acceptable to talk on a cell phone during class?

Yes, the result implies that students and faculty consider it acceptable to talk on a cell phone during class.

No, the result does not imply that students and faculty consider it acceptable to talk on a cell phone during class. In fact, the sample mean ratings indicate that only faculty feel the behavior is appropriate.    

No, the result does not imply that students and faculty consider it acceptable to talk on a cell phone during class. However, the sample mean ratings indicate that both groups feel the behavior is appropriate.

No, the result does not imply that students and faculty consider it acceptable to talk on a cell phone during class. In fact, the sample mean ratings indicate that both groups feel the behavior is inappropriate.

No, the result does not imply that students and faculty consider it acceptable to talk on a cell phone during class. In fact, the sample mean ratings indicate that only students feel the behavior is appropriate.

Answer 1

(a)

(i)

Let

Sample 1 = Students

Sample 2 = Faculty

Given:

n1 = 173

1 = 2.84

s1 = 1

n2 = 98

2 = 3.62

s2 = 1

Since s1 = s2 = 1, the Pooled SD = s_P = 1

Test Statistic is given by:

t = (2.84-3.62)/0.1264

= - 6.17

So,

t = - 6.17

(ii)

ndf = n1 + n2 - 2 = 173 + 98 - 2 = 269

So,

df = 269

(iii)

Two Tail Test

By Technology, P - Value = 0.000

Correct option:

We reject H₀. We have convincing evidence that the mean appropriateness score assigned to wearing a hat in class differs for students and faculty.

(b)

(i)

Let

Sample 1 = Students

Sample 2 = Faculty

Given:

n1 = 173

1 = 2.92

s1 = 1

n2 = 98

2 = 2.12

s2 = 1

Since s1 = s2 = 1, the Pooled SD = s_P = 1

Test Statistic is given by:

t = (2.92-2.12)/0.1264

= 6.33

So,

t = 6.33

(ii)

ndf = n1 + n2 - 2 = 173 + 98 - 2 = 269

So,

df = 269

(iii)

One Tail Test

By Technology, P - Value = 0.000

Correct option:

We reject H₀. We have convincing evidence that the mean appropriateness score assigned to addressing an instructor by their first name is greater for students than for faculty.  

(c)

Let

Sample 1 = Students

Sample 2 = Faculty

Given:

n1 = 173

1 = 1.10

s1 = 1

n2 = 98

2 = 1.08

s2 = 1

Since s1 = s2 = 1, the Pooled SD = s_P = 1

Test Statistic is given by:

t = (1.10-1.08)/0.1264

= 0.16

So,

t = 0.16

(ii)

ndf = n1 + n2 - 2 = 173 + 98 - 2 = 269

So,

ndf = 269

(iii)

Two Tail Test

By Technology, P - Value = 0.874

(iii)

Correct option:

We do not reject H₀. We do not have convincing evidence that the mean appropriateness score assigned to talking on a cell phone in class differs for students and faculty.

(d)

Correct option:

No, the result does not imply that students and faculty consider it acceptable to talk on a cell phone during class. However, the sample mean ratings indicate that both groups feel the behavior is appropriate.