Question

Does the location of your seat in a classroom play a role in attendance or grade? students in a physics
course were randomly assigned to one of four groups. The 400 students in group 1 sat 0 to 4 meters from the front
of the class, the 400 students in group 2 sat 4 to 6.5 meters from the front, the 400 students in group 3 sat 6.5 to 9
meters from the front, and the 400 students in group 4 sat 9 to 12 meters from the front. Complete parts (a)through (c).

(a) For the first half of the semester, the attendance for the whole class averaged 83%. So, if there is no effect due
to seat location, we would expect 83% of students in each group to attend. The data show the attendance history
for each group. How many students in each group attended, on average? Is there a significant difference among
the groups in attendance patterns?

Group 1 2 3 4
Attendance 0.84 0.84 0.84 0.80

The number of students who attended in the first group was...

The number of students who attended in the second group was...

The number of students who attended in the third group was...

The number of students who attended in the fourth group was...

What are the hypotheses? (choose a,b, or c)

A. H₀: The average attendance in each group is different from the average
attendance for the class.
H₁: The average attendance in each group is the same as the average
attendance for the class.

B. H₀: The average attendance in each group is the same as the average
attendance for the class.
H₁: The average attendance in each group is different from the average
attendance for the class.

C. None of these.

Compute the P-value.
P-value = (Round to three decimal places as needed.)

Is there a significant difference among the groups in attendance patterns? Use the level of significance α = 0.05.

A. No, H₀. should not be rejected because the P-value of the test is
than α.

B. No.H₀ should not be rejected because the P-value of the test is greater
than α.

C. Yes.H₀ should be rejected because the P-value of the test is greater than α .

D. Yes. H₀ should be rejected because the P-value of the test is less than α.

(b) For the second half of the semester, the groups were rotated so that group 1 students moved to the back of
class and group 4 students moved to the front. The same switch took place between groups 2 and 3. The
attendance for the second half of the semester averaged 80%. The data show the attendance records for the
original groups. How many students in each group attended, on average? Is there a significant difference in
attendance patterns? Use the p-value approach and use the level of significance α = 0.05

Group 1 2 3 4
Attendance 0.84 0.81 0.78 0.77

The number of students who attended in the first group was...

The number of students who attended in the second group was...

The number of students who attended in the third group was...

The number of students who attended in the fourth group was...

The wording of the hypotheses is the same as part (a).

Compute the P-value for the test with technology and compare to the level of significance α = 0.05.
P-value = (Round to three decimal places as needed.)

Is there a significant difference in attendance patterns? (choose a,b,c,or d)

A. Yes , because the P-value of the test is than the level of significance.

B. Yes, because the P-value of the test is greater than the level of significance.

C. No, because the P-value of the test is less than the level of significance.

D. No, because the P-value of the test is greater than the level of significance.

(c) At the end of the semester, the proportion of students in the top 20% of the class was determined. Of the
students in group 1, 25% were in the top 20%; of the students in group 2, 20% were in the top 20%; of the students
in group 3, 16% were in the top 20%; of the students in group 4, 19% were in the top 20% . How many students would we expect to be in the top 20% of the class if seat location plays no role in grades?

The number of students expected to be in the top 20% of the class in group 1 if seat location plays no role on
grades is...

The number of students expected to be in the top 20% of the class in group 2 is...

The number of students expected to be in the top 20% of the class in group 3 is...

The number of students expected to be in the top 20% of the class in group 4 is...

What is the null hypothesis?

A. H₀: The number of students in the top 20% in each group would be the same amongst the groups. H₁: The number of students in the top 20% in each group would not be the same amongst the groups.

B. None of these.

C. H₀: The number of students in the top 20% in each group would not be
the same amongst the groups. H1: The number of students in the top 20% in each group would be the
same amongst the groups

Compute the P-value for the test with technology and compare to the level of significance α = 0.05.
P-value = (Round to three decimal places as needed.)

Is there a significant difference in the number of students in the top 20% of the class by group? (choose a,b,c, or d)
A. No. H₀ should not be rejected because the P-value of the test is greater than the level of significance.

B. Yes. H₀ should be rejected because the P-value of the test is less than the level of significance.

C. No .H₀ should not be rejected because the P-value of the test is less than the level of significance

D. Yes. H₀ should be rejected because the P-value of the test is greater than the level of significance.

Answer 1

By definition of proportion,

p = No. of favorable cases / Total No. of cases

(a) Here, for Group 1,

Similar figures would be obtained for Group 2 and 3.

For Group 4:

Hence,

The number of students who attended in the first group was 336

The number of students who attended in the second group was 336

The number of students who attended in the third group was 336

The number of students who attended in the fourth group was 320

We are asked to test whether there is a significant difference among the groups in attendance patterns. The claim to be tested is usually taken to be the alternative hypothesis and the negation of the claim (containing the "=" equality is taken to be the null).The correct option would be:

B. H₀: The average attendance in each group is the same as the average attendance for the class.
H₁: The average attendance in each group is different from the average attendance for the class.

The appropriate statistical test to test the above hypothesis would be a Chi-square test of Goodness of fit, with test statistic given by,

where O_i and E_i denote the observed and expected frequencies respectively. As stated in the null hypothesis, we would expect the attendance in each group to be equal i.e 0.83 x 1600 = 1328 to be equally divided among the four groups - Each group is expected to have an attendance of 1328 / 4 = 332 students.

Substituting the values in the test statistic,

= 0.58

The p-value of the test can be quickly obtained using the excel function for n - 1 = 4 - 1 = 3 degrees of freedom at 5% level of significance:

We get p-value = 0.901 > > 0.05. Hence, the correct option would be:

B. No.H₀ should not be rejected because the P-value of the test is greater than α.

We may conclude that the data does not provide sufficient evidence to support the claim that there is a significant difference among the groups in attendance patterns.

(b)

Here, for Group 1,

Group 2:

Group 3:

For Group 4:

Hence,

The number of students who attended in the first group was 336

The number of students who attended in the second group was 324

The number of students who attended in the third group was 312

The number of students who attended in the fourth group was 308

The appropriate statistical test to test if there is a significant difference among the groups in attendance patterns. would be a Chi-square test of Goodness of fit, with test statistic given by,

where O_i and E_i denote the observed and expected frequencies respectively. As stated in the null hypothesis, we would expect the attendance in each group to be equal i.e 0.80 x 1600 = 1280 to be equally divided among the four groups - Each group is expected to have an attendance of 1280 / 4 = 320 students.

Substituting the values in the test statistic,

= 1.50

The p-value of the test for n - 1 = 4 - 1 = 3 degrees of freedom at 5% level of significance is obtained as:

P-value = 0.682

We get p-value = 0.682 > > 0.05. Hence, the correct option would be:

D. No, because the P-value of the test is greater than α.

We may conclude that the data does not provide sufficient evidence to support the claim that there is a significant difference among the groups in attendance patterns.

(c) If seat location played no role, we would expect the the overall 20% to be equally distributed among the four groups 0.20 x 1600 = 320 i.e each of the 40 groups would contain 320 / 4 = 80.

Hence,

The number of students expected to be in the top 20% of the class in group 1 if seat location plays no role on grades is 80

The number of students expected to be in the top 20% of the class in group 2 is 80

The number of students expected to be in the top 20% of the class in group 3 is 80

The number of students expected to be in the top 20% of the class in group 4 is 80

The appropriate set of hypothesis would be:

A. H₀: The number of students in the top 20% in each group would be the same amongst the groups. H₁: The number of students in the top 20% in each group would not be the same amongst the groups.

Here,

O₁ = 0.25 x 400 = 100, O₂ = 0.20 x 400 = 80,O₃ = 0.16 x 400 = 64, O₄ = 0.19 x 400 = 76

Substituting the values in the test statistic,

= 8.4

The p-value of the test for n - 1 = 4 - 1 = 3 degrees of freedom at 5% level of significance is obtained as:

P-value = 0.038

We get p-value = 0.038 < 0.05. Hence, the correct option would be:

B. Yes. H₀ should be rejected because the P-value of the test is less than the level of significance.