To test his hypothesis that students who finish an exam first get better grades,
ID: 3390752 • Letter: T
Question
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.)
Explanation / Answer
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
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