Question
In: Statistics and Probability
We draw a random sample of size 49 from a normal population with variance 2.1. If...
We draw a random sample of size 49 from a normal population with variance 2.1. If the sample mean is 21.5, what is a 99% confidence interval for the population mean?
Solutions
Expert Solution
Solution :
Given that,
Sample size = n = 49
Z
/2
= 2.576
Margin of error = E = Z/2*
(
/
= 2.576 * (1.4491 /
Margin of error = E = 0.5
At 99% confidence interval estimate of the population mean is,
- E < 
<
+ E
21.5 - 0.5 <
< 21.5 + 0.5
21 <
< 22
(21 , 22)
orchestra answered 2 years agoRelated Solutions
Random sample of size 7 is drawn from a normal population with variance 2.5 the sample...
Random sample of size 7 is drawn from a normal population with
variance 2.5 the sample observations are 9, 16, 10, 14, 8, 13, 14.
find 99% confidence interval for the population mean what would be
the confidence interval if the variance is unknown.
We draw a random sample of size 36 from a population with standard deviation 3.2. If...
We draw a random sample of size 36 from a population with
standard deviation 3.2. If the sample mean is 27, what is a 95%
confidence interval for the population mean?
[26.7550, 28.2450]
[25.9547, 28.0453]
[25.8567, 28.1433]
[26.8401, 27.1599]
We draw a random sample of size 36 from a population with standard deviation 3.2. If...
We draw a random sample of size 36 from a population with
standard deviation 3.2. If the sample mean is 27, what is a 95%
confidence interval for the population mean?
Say that a sample of size 49 taken from a normally distributed population, has variance =...
Say that a sample of size 49 taken from a normally distributed
population, has variance = 1. The sample has a mean of 0.49. Then,
a 95% confidence interval for µ will be
0.49 – (1.96)(1/7) < µ < 0.49 + (1.96)(1/7)
0.49 – (2.575)(1/7) < µ < 0.49 + (1.96)(1/7)
49 – (1.96)(1/0.7) < µ < 49 + (1.96)(1/0.7)
49 – (2.575)(1/0.7) < µ < 49 + (2.575)(1/0.7)
4 We draw a random sample of size 40 from a population with standard deviation 2.5....
4
We draw a random sample of size 40 from a population with standard
deviation 2.5.
Show work in excel with formulas
a
If the
sample mean is 27, what is a 95% confidence interval for the
population mean?
b
If the
sample mean is 27, what is a 99% confidence interval for the
population mean?
c
If the
sample mean is 27, what is a 90% confidence interval for the
population mean?
d
If the
sample mean is 27...
The sample variance of a random sample of 50 observations from a normal population was found...
The sample variance of a random sample of 50 observations from
a normal population was found to be s2 = 80. Can we
infer at the 1% significance level (i.e., a = .01) that the
population variance is less than 100 (i.e., x < 100) ?
Repeat part a changing the sample size to 100
What is the affect of increasing the sample size?
7.A random sample of 49 observations is drawn from a population with a normal distribution. If...
7.A random sample of 49 observations is drawn from a population
with a normal distribution. If the sample mean is 265 and the
sample standard deviation is 57, find the 95% confidence interval
for the population mean.
8. A random sample of 49 observations is drawn from a population
with a normal distribution with a standard deviation of 57. If the
sample mean is 265, find the 95% confidence interval for the
population mean. Compare this confidence interval with the...
Suppose we take a random sample X1,…,X5 from a normal population with unknown variance σ2 and...
Suppose we take a random sample X1,…,X5 from a normal population
with unknown variance σ2 and unknown mean μ. We test the
hypotheses
H0:σ=2 vs. H1:σ<2
and we use a critical region of the form {S2<k} for some
constant k.
(1) - Determine k so that the type I error probability α of the
test is equal to 0.05.
(2) - For the value of k found in part (1), what is your
conclusion in this test if you see...
Suppose we take a random sample X1,…,X5 from a normal population with an unknown variance σ2...
Suppose we take a random sample X1,…,X5 from a normal population
with an unknown variance σ2 and unknown mean μ.
Construct a two-sided 95% confidence interval for σ2 if the
observations are given by
−1.25,1.91,−0.09,2.71,2.70
Suppose we take a random sample X1,…,X7 from a normal population with an unknown variance σ21...
Suppose we take a random sample X1,…,X7 from a normal population
with an unknown variance σ21 and unknown mean μ1. We also take
another independent random sample Y1,…,Y6 from another normal
population with an unknown variance σ22 and unknown mean μ2.
Construct a two-sided 90% confidence interval for σ21/σ22 if the
observations are as follows: from the first population we
observe
3.50,0.64,2.68,6.32,4.04,1.58,−0.45
and from the second population we observe
1.85,1.53,1.57,2.13,0.74,2.17
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- What is the difference between the conversion value and conversion premium?
- Special Order Total cost data follow for Glendale Manufacturing Company, which has a normal capacity per...
- Carbex, Inc., produces cutlery sets out of high-quality wood and steel. The company makes a standard...
- 6)explain some of the positive and negative effects a secondary ticket market can have a on...
- The speed at which a processor can process instructions can be increased by making its clock...
- Bonomo Corporation’s bonds have 4 years remaining to maturity. Interest is paid annually in arrears. The...
- What is a good response to discussion below: The crowdfunding site I chose to use is...
ADVERTISEMENT