Assignment:
Q1. A hearing aid battery manufacturer claims that the battery's mean lifetime is at least 20 days. We will take sample of 16 batteries to test
H0 μ ≤ 20
Ha0 μ ≥ 20 a = 0.025
What is the test statistic?
What is the critical region? Reject H0 if
What is the definition of a?
a. Deciding that manufacture's claim is true when it is not true
b. Deciding that manufacture's claim is not true when it is true
Data:
Sixteen hearing aid batteries tested had the following lifetimes
17 16 18 19 20 15 14 17 19 20 21 22 17 15 18 14
Σx Σx2
x‾ s2 s
What is the value of the test statistic?
What is the decision ? a. Reject H. b. AcceptH.
What is the decision in terms of the problem?
a. manufacture's claim is true (mean lifetime is at least 20 days)
b. manufacture's claim is not true( mean lifetime is not at least 20 days)
What is the 95% confidence interval forμ
Q2. The blood pressure of 12 people was taken before and after stopping smoking
|
Person
|
Before
|
After
|
d
|
d*d
|
|
1
|
146
|
120
|
26
|
|
|
2
|
138
|
124
|
14
|
|
|
3
|
160
|
132
|
28
|
|
|
4
|
130
|
110
|
20
|
|
|
5
|
135
|
123
|
12
|
|
|
6
|
128
|
132
|
-4
|
|
|
7
|
134
|
105
|
29
|
|
|
8
|
160
|
140
|
20
|
|
|
9
|
150
|
112
|
38
|
|
|
10
|
138
|
112
|
26
|
|
|
11
|
126
|
97
|
29
|
|
|
12
|
165
|
146
|
19
|
|
|
|
|
|
|
|
Test the hypotheses that
H0 μd ≤10
Ha μd > 10 α = 0.05
Test Statistic:
Critical Region: Reject ; if_________
Value of test statistic=_________
What is the decision:? a. Reject H0 b. Accept H0
What is the decision in terms of the problem?
a. Blood pressure medicine reduces blood pressure by at least 10
b. Blood pressure medicine does not reduce blood pressure by at least 10
Q3. A sample of 15 teachers from Rhode Island has an average salary of $35,270, with a standard deviation of $3256. A sample of 16 teachers from New York has an average salary of $29,512, with a standard deviation of $1432. Is there a significant difference in teachers' salaries between the two states? Use a = 0.02. Find the 99% confidence interval for the difference of the two means.
Test the hypotheses that Ho 1.1R1 PNY
H0 μRI= μNY
Ha μRI≠ μNY
Test Statistic:
Critical Region: Reject Ho if
Value of the test statistic :
Decision: What is the decision:? a. Reject Ho b. AcceptHo
What is the decision in terms of the problem?
a. Salaries are different b. Salaries are not different.
Find the 99% confidence interval for the difference of two means