Question
In: Statistics and Probability
Question3: Consider the following 14 independent measurements from a normal distribution: Independent measurements 20 18 11...
Question3: Consider the following 14 independent measurements
from a normal distribution:
Independent measurements
20 18 11 20 16 14 15 15 14 13 11 18 20 9
1) What is the standard error of the sample mean?
0.9936
3.5826
0.9575
3.4303
2) Calculate a 99% confidence interval for the population
mean.
[5.8831,24.6883]
[12.9734,17.5980]
[12.4015,18.1700]
[12.7480,17.8234]
Solutions
Expert Solution
 |
 |
 |
| 20 | 4.7142857 | 22.22448980 |
| 18 | 2.7142857 | 7.36734694 |
| 11 | -4.2857143 | 18.36734694 |
| 20 | 4.7142857 | 22.22448980 |
| 16 | 0.7142857 | 0.51020408 |
| 14 | -1.2857143 | 1.65306122 |
| 15 | -0.2857143 | 0.08163265 |
| 15 | -0.2857143 | 0.08163265 |
| 14 | 1.2857143 | 1.65306122 |
| 13 | -2.2857143 | 5.22448980 |
| 11 | -4.2857143 | 18.36734694 |
| 18 | 2.7142857 | 7.36734694 |
| 20 | 4.7142857 | 22.22448980 |
| 9 | -6.2857143 | 39.51020408 |
 |
 |
a) The standard error of the sample mean
Answer: 0.9575
b) We need to construct the 99% confidence interval for the population mean μ.
The critical value for α=0.01 and df = n-1 =14-1= 13, tc= t1−α/2;n−1=3.012.
The corresponding confidence interval is computed as shown below:
Answer: (12.4015, 18.1700)
orchestra answered 2 years agoRelated Solutions
The following sample data are from a normal population: 13, 11, 15, 18, 16, 14, 9,...
The following sample data are from a normal population: 13, 11,
15, 18, 16, 14, 9, 8.
(a)
What is the point estimate of the population mean?
(b)
What is the point estimate of the population standard deviation?
(Round your answer to three decimal places.)
(c)
With 95% confidence, what is the margin of error for the
estimation of the population mean? (Round your answer to one
decimal place.)
(d)
What is the 95% confidence interval for the population mean?...
11. (20) GPA distribution in UPW university is a normal distribution with an average of 2.68...
11.
(20) GPA distribution in UPW
university is a normal distribution with an average of 2.68 and a
standard deviation of 0.4.
(a) About what
proportion of the students have GPA at most 3?
(b) About what
proportion of the students’ GPA are between 2 and 3?
(c) The President of
the university is establishing a new scholarship, the minimum
qualification is that students GPA have to be among top 3%, what is
the numerical GPA a student must have...
11. (20) GPA distribution in UPW university is a normal distribution with an average of 2.68...
11.
(20) GPA distribution in UPW
university is a normal distribution with an average of 2.68 and a
standard deviation of 0.4.
(a) About what
proportion of the students have GPA at most 3?
(b) About what
proportion of the students’ GPA are between 2 and 3?
(c) The President of
the university is establishing a new scholarship, the minimum
qualification is that students GPA have to be among top 3%, what is
the numerical GPA a student must have...
Low Medium High 14 18 16 6 17 20 11 23 18 12 17 16 11...
Low
Medium
High
14
18
16
6
17
20
11
23
18
12
17
16
11
10
15
9
20
16
6
15
16
12
17
17
14
25
11
11
11
13
4
18
22
9
18
16
7
20
10
12
21
18
12
27
9
17
13
19
11
22
16
8
17
12
Our worksheets lists the number of 3+ syllable words in each
magazine grouped by education level. Use your spreadsheet program
to conduct a...
Check that the measurements for the heart rate are coming from a normal distribution by constructing...
Check that the measurements for the heart rate are coming from
a normal distribution by constructing a histogram.
Create indicator variables for female and good AQI. Fit the
regression model and discuss its goodness of fit. What portion of
variation in heart rate can this model explain?
Write the fitted model. What variables are significant
predictors of heart rate at the 5% level of significance?
Plot residuals against predicted values. Does it show any
pattern?
Compute the predicted heart rate...
Suppose that the pH measurements of the field from the question above follow a normal distribution...
Suppose that the pH measurements of the field from the question
above follow a normal distribution with mean 11 pH and standard
deviation 2 pH. What is the probability that the engineer obtains a
sample mean (with n = 5) greater than 11.8 pH? Assume each
measurement is independent of each other.
The following sample data are from a normal population: 10, 9, 12, 14, 13, 11, 6,...
The following sample data are from a normal population: 10, 9,
12, 14, 13, 11, 6, 5.
a. What is the point estimate of the population mean?
b. What is the point estimate of the population standard
deviation (to 2 decimals)?
c. With 95% confidence, what is the margin of error for the
estimation of the population mean (to 1 decimal)?
d. What is the 95% confidence interval for the population mean
(to 1 decimal)?
( , )
The following sample data are from a normal population: 10, 9, 12, 14, 13, 11, 7,...
The following sample
data are from a normal population: 10, 9, 12, 14, 13, 11, 7, 4.
a. What is the point
estimate of the population mean?
b. What is the point
estimate of the population standard deviation (to 2 decimals)?
c. With 95%
confidence, what is the margin of error for the estimation of the
population mean (to 1 decimal)?
d. What is the 95%
confidence interval for the population mean (to 1 decimal)?
( , )
Suppose you have selected a random sample of ?=13 measurements from a normal distribution. Compare the...
Suppose you have selected a random sample of ?=13 measurements
from a normal distribution. Compare the standard normal z values
with the corresponding t values if you were forming the following
confidence intervals.
a) 80% confidence interval
?=
?=
(b) 90% confidence interval
?=
?=
(c) 99% confidence interval
?=
?=
Consider independent random samples from two populations that are normal or approximately normal, or the case...
Consider independent random samples from two populations that
are normal or approximately normal, or the case in which both
sample sizes are at least 30. Then, if σ1 and
σ2 are unknown but we have reason to believe
that σ1 = σ2, we can pool
the standard deviations. Using sample sizes n1
and n2, the sample test statistic
x1 − x2 has a Student's
t distribution where
t =
x1 − x2
s
1
n1
+
1
n2
with degrees...
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- What 2 things happen to the melting point of a solid when an impurity is present?
- How Can Hominin Evolution be characterized as " mosaic evolution" Use examples of species from the...
- Absorption and Variable Costing Income Statements for Two Months and Analysis During the first month of...
- Mobile and wireless devices are being increasingly used in the Business Administration and Management Industry. write...
- What are the options that might be considered in relation to introducing flexible work practices? What...
- Question 2 : Aggregate Scores: Write a program that opens 2 files, quiz.txt, and hw.txt. The...
- Define the term symbiosis specifically as it applies in a biological context. Compare and contrast parasitism,...
ADVERTISEMENT