To test his hypothesis that students who finish an exam firs

To test his hypothesis that students who finish an exam first get better grades, a professor kept track of the order in which papers were handed in. Of the first 25 papers, 10 received a B or better compared with 8 of the last 24 papers handed in.

(a-1)  

(a-2)  

Specify the decision rule at = .10. (Round your answer to 2 decimal places).

Reject the null hypothesis if zcalc > _______.

(a-3)  

Find the test statistic zcalc and p-value. (Do not round the intermediate calculations. Round the proportions to 4 decimal places. Round your final answers to 4 decimal places.)

Solution

To test his hypothesis that students who finish an exam first get better grades, a professor kept track of the order in which papers were handed in. Of the first 25 papers, 10 received a B or better compared with 8 of the last 24 papers handed in.

(a-1)  

Choose the appropriate hypotheses. Let 1 represent the grades of the first group and 2 represent the grades of the second group.

            a. H0: 1 – 2 0 vs. H1: 1– 2 < 0.

            b. H0: 1 – 2 0 vs. H1: 1– 2 > 0.

(a-2)  

Specify the decision rule at = .10. (Round your answer to 2 decimal places).

Reject the null hypothesis if zcalc > 1.28

(a-3)  

Find the test statistic zcalc and p-value. (Do not round the intermediate calculations. Round the proportions to 4 decimal places. Round your final answers to 4 decimal places.)

Z calc =0.4839

P= 0.3142

Calculated z=0.4839 < 1.28 the table value

The null hypothesis is not rejected.

There is insufficient evidence to conclude that students who finish an exam first get better grades.

Z Test for Differences in Two Proportions

Data

Hypothesized Difference

0

Level of Significance

0.1

Group 1

Number of Items of Interest

10

Sample Size

25

Group 2

Number of Items of Interest

8

Sample Size

24

Intermediate Calculations

Group 1 Proportion

0.4

Group 2 Proportion

0.3333

Difference in Two Proportions

0.0667

Average Proportion

0.3673

Z Test Statistic

0.4839

Upper-Tail Test

Upper Critical Value

1.28

p-Value

0.3142

Do not reject the null hypothesis

Z Test for Differences in Two Proportions
Data
Hypothesized Difference	0
Level of Significance	0.1
Group 1
Number of Items of Interest	10
Sample Size	25
Group 2
Number of Items of Interest	8
Sample Size	24
Intermediate Calculations
Group 1 Proportion	0.4
Group 2 Proportion	0.3333
Difference in Two Proportions	0.0667
Average Proportion	0.3673
Z Test Statistic	0.4839
Upper-Tail Test
Upper Critical Value	1.28
p-Value	0.3142
Do not reject the null hypothesis