Question
In: Statistics and Probability
Use the following for questions 2 and 3. A simple random sample of 30 items was...
Use the following for questions 2 and 3. A simple random sample of 30 items was selected. The sample mean was 15 and the population standard deviation is known to be 6. What is a 90% confidence interval for the population mean?
Is it reasonable to conclude that the population mean could 14?
Yes, because 14 is in the confidence interval
Yes, because 14 is not in the confidence interval
No, because 14 is in the confidence interval
No, because 14 is not in the confidence interval
Solutions
Expert Solution
Solution:
Note that, Population standard deviation()
is known. So we use z distribution.
Our aim is to construct 90% confidence interval.
c = 0.90
= 1- c = 1- 0.90 = 0.10
/2
= 0.10
2 = 0.05 and 1-
/2 = 0.950
Search the probability 0.950 in the Z table and see corresponding z value
=
1.645
The margin of error is given by
E = /2
* (
/
n )
= 1.645 * (6 /
30)
= 1.802
Now , confidence interval for mean()
is given by:
(
- E ) <
< (
+ E)
(15 - 1.802) <
< (15 + 1.802)
13.198 <
< 16.802
(13.198 , 16.802 )
Is it reasonable to conclude that the population mean could 14?
Yes, because 14 is in the confidence interval
orchestra answered 1 year agoRelated Solutions
A simple random sample of 30 items resulted in a sample mean of 30. The population...
A simple random sample of 30 items resulted in a sample mean of
30. The population standard deviation is 15.
a. Compute the 95% confidence interval for the
population mean. Round your answers to one decimal place.
( , )
b. Assume that the same sample mean was
obtained from a sample of 120 items. Provide a 95% confidence
interval for the population mean. Round your answers to two decimal
places.
( , )
A simple random sample of 30 items resulted in a sample mean of25. The population...
A simple random sample of 30 items resulted in a sample mean of
25. The population standard deviation is 7 . Round your answers to
two decimal places
a. What is the standard error of the mean,
?
b. At 95% confidence, what is the margin of
error?
A simple random sample of 70 items resulted in a sample mean of 60. The population...
A simple random sample of 70 items resulted in a sample mean of
60. The population standard deviation is σ = 15.
(a) Compute the 95% confidence interval for the population mean.
(Round your answers to two decimal places.)
_________ to _________
(b) Assume that the same sample mean was obtained from a sample
of 140 items. Provide a 95% confidence interval for the population
mean. (Round your answers to two decimal places.)
_________ to _________
(c) What is the...
A simple random sample of 60 items resulted in a sample mean of 80. The population...
A simple random sample of 60 items resulted in a sample mean of
80. The population standard deviation is
σ = 5.
(a)
Compute the 95% confidence interval for the population mean.
(Round your answers to two decimal places.)
to
(b)
Assume that the same sample mean was obtained from a sample of
120 items. Provide a 95% confidence interval for the population
mean. (Round your answers to two decimal places.)
to
A simple random sample of 60 items resulted in a sample mean of 80. The population...
A simple random sample of 60 items resulted in a sample mean of
80. The population standard deviation is
σ = 5.
(a)
Compute the 95% confidence interval for the population mean.
(Round your answers to two decimal places.)
to
(b)
Assume that the same sample mean was obtained from a sample of
120 items. Provide a 95% confidence interval for the population
mean. (Round your answers to two decimal places.)
to
A simple random sample of 60 items resulted in a sample mean of 65. The population...
A simple random sample of 60 items resulted in a sample mean of
65. The population standard deviation is 16. a. Compute the 95%
confidence interval for the population mean (to 1 decimal). ( , )
b. Assume that the same sample mean was obtained from a sample of
120 items. Provide a 95% confidence interval for the population
mean (to 2 decimals). ( , ) c. What is the effect of a larger
sample size on the margin of...
A simple random sample of 60 items resulted in a sample mean of 65. The population...
A simple random sample of 60 items resulted in a sample mean of
65. The population standard deviation is 16. a. Compute the 95%
confidence interval for the population mean (to 1 decimal). ( , )
b. Assume that the same sample mean was obtained from a sample of
120 items. Provide a 95% confidence interval for the population
mean (to 2 decimals). ( , ) c. What is the effect of a larger
sample size on the margin of...
simple random sample of 80 items from a population with = 8 resulted in a sample...
simple random sample of 80 items from a population with = 8
resulted in a sample mean of 38. If required, round your answers to
two decimal places. a. Provide a 90% confidence interval for the
population mean. to b. Provide a 95% confidence interval for the
population mean. to c. Provide a 99% confidence interval for the
population mean. to
A simple random sample of 60 items resulted in a sample mean of 95. The population...
A simple random sample of 60 items resulted in a sample mean of
95. The population standard deviation is 13.
a. Compute the 95% confidence interval for the population mean
(to 1 decimal).
( , )
b. Assume that the same sample mean was obtained from a sample
of 120 items. Provide a 95% confidence interval for the population
mean (to 2 decimals).
( , )
c. What is the effect of a larger sample size on the margin of
error?
SelectIt increasesIt decreasesIt...
A simple random sample of 60 items resulted in a sample mean of 10. The population...
A simple random sample of 60 items resulted in a sample mean of
10. The population standard deviation is 20.
Compute the 95% confidence interval for the population mean.
Round to 1 decimal place.
Assume that the same sample mean was obtained from a sample of
120 items. Provide a 95% confidence interval for the population
mean. Round to 2 decimal places.
What is the effect of a larger sample size on the interval
estimate? Larger sample provides a larger...
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- NPV Your division is considering two projects with the following cash flows (in millions): 0...
- The equivalent synchronous impedance of a 25kVA, 400V three-phase Y-connected synchronous generator is 0.05 + j1.6...
- You have $100,000 to invest in either Stock D, Stock F, or a risk-free asset. You...
- In two or three sentences, explain how you have seen the concept of grit work in...
- You have invested 30 percent of your portfolio in Jacob, Inc., 40 percent is Bella Co.,...
- Parallel Arrays This question is in MindTap Cengage Summary In this lab, you use what you...
- 5. You have invested 30 percent of your portfolio in Jacob, Inc., 40 percent is Bella...
ADVERTISEMENT