Homework Sourse1 The principal of Berkeley High School has read that on ave
1. The principal of Berkeley High School has read that, on average, a high school student will miss 15 days of class per school year. He is curious if his high school is letting students have too many sick days, so he takes a random sample of 40 students\' attendence records, and finds that the sample average is 22 days missed with a sample standard deviation of 8 days. If he decides to test the hypothesis H0: mu = 15 days against Ha: mu not = 15 days using this sample, what distribution does he use and what p-value does he find?
Select one:
a. He uses the T distribution with 40 degrees of freedom, and finds a p-value of less than 0.05.
b. He uses the T distribution with 40 degrees of freedom, and finds a p-value greater than 0.01.
c. He uses the T distribution with 39 degrees of freedom, and finds a p-value between 0.01 and 0.05.
d. He uses the T distribution with 39 degrees of freedom, and finds a p-value of less than 0.05.
e. He uses the T distribution with 29 degrees of freedom, and finds a p-value greater than 0.01.
2. The principal of Berkeley High School has read that based on the national norm, a high school student will miss 15 days of class per school year. He is curious if the number of day missed by the students in his school is different from the national norm. He takes a random sample of 25 students\' attendence records, and finds that for this sample the average number of school days missed per year is 17 and the standard deviation is 8. What is the approximate p-value for a two-tailed test?
Solution
t Test for Hypothesis of the Mean
Data
Null Hypothesis mean=
15
Level of Significance
0.05
Sample Size
40
Sample Mean
22
Sample Standard Deviation
8
Intermediate Calculations
Standard Error of the Mean
1.2649
Degrees of Freedom
39
t Test Statistic
5.5340
Two-Tail Test
Lower Critical Value
-2.0227
Upper Critical Value
2.0227
p-Value
0.0000
Reject the null hypothesis
Select one:
a. He uses the T distribution with 40 degrees of freedom, and finds a p-value of less than 0.05.
b. He uses the T distribution with 40 degrees of freedom, and finds a p-value greater than 0.01.
c. He uses the T distribution with 39 degrees of freedom, and finds a p-value between 0.01 and 0.05.
d. He uses the T distribution with 39 degrees of freedom, and finds a p-value of less than 0.05.
e. He uses the T distribution with 29 degrees of freedom, and finds a p-value greater than 0.01.
2. The principal of Berkeley High School has read that based on the national norm, a high school student will miss 15 days of class per school year. He is curious if the number of day missed by the students in his school is different from the national norm. He takes a random sample of 25 students\' attendence records, and finds that for this sample the average number of school days missed per year is 17 and the standard deviation is 8. What is the approximate p-value for a two-tailed test?
t Test for Hypothesis of the Mean
Data
Null Hypothesis mean =
15
Level of Significance
0.05
Sample Size
25
Sample Mean
17
Sample Standard Deviation
8
Intermediate Calculations
Standard Error of the Mean
1.6000
Degrees of Freedom
24
t Test Statistic
1.2500
Two-Tail Test
Lower Critical Value
-2.0639
Upper Critical Value
2.0639
p-Value
0.2234
Do not reject the null hypothesis
The required P=0.2234
| t Test for Hypothesis of the Mean | |
| Data | |
| Null Hypothesis mean= | 15 |
| Level of Significance | 0.05 |
| Sample Size | 40 |
| Sample Mean | 22 |
| Sample Standard Deviation | 8 |
| Intermediate Calculations | |
| Standard Error of the Mean | 1.2649 |
| Degrees of Freedom | 39 |
| t Test Statistic | 5.5340 |
| Two-Tail Test | |
| Lower Critical Value | -2.0227 |
| Upper Critical Value | 2.0227 |
| p-Value | 0.0000 |
| Reject the null hypothesis |
