Homework
6 (50 pts) Due 10/8

Primarylecture recording: topic 7
[Review
Question]:In
your own words, explain what the margin error is? How do the confidence level,
sample size and population stand deviation (sigma) affect the margin error?
[Review
Question]:How to explain the statement the 95%
confidence interval is [1,3]? Justify each of the following interpretation
(why it is right or wrong?)
A)
95% of the values in the population is between 1 and 3.
B)
95% of the values in the sample is between 1 and 3.
C)
95% of sample means in the sampling distribution is between 1 and 3.
D)
95% of population mean is between 1 and 3.

[Review
Question]:List conditions (assumptions) for the
z-method and t-method, and then point what the major difference between the
two.
[Review
Question]:What is standard error and what does it
measure? Do you want a smaller or bigger standard error in general?

StatsPortal>Statistical videos: StatClips: sampling
distributions: overview and motivation part II
[Review
Question]:Given.0/msohtmlclip1/01/clip_image002.gif”> and.0/msohtmlclip1/01/clip_image004.gif”>, what is the mean and standard deviation of the sample
mean? I.e.,.0/msohtmlclip1/01/clip_image006.gif”> and.0/msohtmlclip1/01/clip_image008.gif”>.

[Review
Question]:CLT is based on multiple samples, and
sampling distribution. But in a real study, we have only data from one sample,
how can we use a single sample to estimation the population parameter?

StatsPortal>assignment> Stattutor: margin of error
and confidence interval
[Review Question]:A 90% confidence
interval for is (11.5, 12.3). What is the probability that the value of is
in this interval?

[Review
Question]:The higher the level of confidence you
choose, the ____(more/less) sure you can be that mu will be in the confidence
interval. The _____(more/less) precise, or _____(wider/narrower) you interval
will be.

1. A shipment of 1000
small lab mice arrives at the animal care facility with the weight following a skewed distribution (.0/msohtmlclip1/01/clip_image010.gif”>. A sample of 40
mice is selected and weighed. The sample average weight is 10.2 g, and the
sample standard deviation is 2 g.

a. What are the
population and sample in this question?
b. Since we know the.0/msohtmlclip1/01/clip_image012.gif”>, we can compute the confidence interval with the Z-method. What is the
margin error?
c. Compute and
interpret a 90% confidence interval
for the mean weight of all the mice in the shipment.

2. What critical value t* would you use for a confidence interval for
the mean of the population in each of the following situations?
a. A 95% confidence interval based on n=10 observations.
b. A 99% confidence interval from an simple random sample of 20
observations.
c. An 80% confidence interval from a sample of size 7

3.
A student in wildlife management
studied trout habitat in the upper Shavers Fork watershed in West Virginia. The
springtime water pH of 29 randomly selected tributary sample sites was found to
have the following values:6

.0/msohtmlclip1/01/clip_image013.gif” alt=”http://ebooks.bfwpub.com/psls3e/tables/17_T_UN_4.gif”>
a.
What is the standard error of the mean.
b.
Use a 90% confidence interval to
estimate the mean springtime water pH of the tributary water basin around the
Shavers Fork watershed
4. A dendritic tree is a branched structure that
emanates from the body of a nerve cell. In a study of brain development,
researchers examined brain tissue from 36 adult guinea pigs. The investigators
randomly selected nerve cells from a certain region of the brain and counted
the number of dendritic branch segments emanating from each selected cell. A
total of 36 cells (1 per pig) was selected, and the resulting counts were as
follows:

measurement

28

24

38

25

42

26

29

45

25

26

49

28

35

47

26

31

35

28

41

46

33

24

26

32

48

35

35

39

53

38

38

59

17

26

44

53

a) Construct a 95% confidence interval for the
population mean of dendrite branch segments (The variable can be seen as
continuous in this case).

b)
Suppose
you want to estimate the population mean to be within 2 cells, how many pigs
should be examed?

7[OQ]
Create a confidence interval
problem and specify why you should use
the Z-method or T-method. Provide solution
to your question and attach your data set.

Homework
6 (50 pts) Due 10/8Primarylecture recording: topic 7[Review
Question]:In
your own words, explain what the margin error is? How do the confidence level,
sample size and population stand deviation (sigma) affect the margin error? [Review
Question]:How to explain the statement the 95%
confidence interval is [1,3]? Justify each of the following interpretation
(why it is right or wrong?)A)
95% of the values in the population is between 1 and 3.B)
95% of the values in the sample is between 1 and 3.C)
95% of sample means in the sampling distribution is between 1 and 3. D)
95% of population mean is between 1 and 3.[Review
Question]:List conditions (assumptions) for the
z-method and t-method, and then point what the major difference between the
two. [Review
Question]:What is standard error and what does it
measure? Do you want a smaller or bigger standard error in general? StatsPortal>Statistical videos: StatClips: sampling
distributions: overview and motivation part II [Review
Question]:Given.0/msohtmlclip1/01/clip_image002.gif”> and.0/msohtmlclip1/01/clip_image004.gif”>, what is the mean and standard deviation of the sample
mean? I.e.,.0/msohtmlclip1/01/clip_image006.gif”> and.0/msohtmlclip1/01/clip_image008.gif”>. [Review
Question]:CLT is based on multiple samples, and
sampling distribution. But in a real study, we have only data from one sample,
how can we use a single sample to estimation the population parameter? StatsPortal>assignment> Stattutor: margin of error
and confidence interval [Review Question]:A 90% confidence
interval for is (11.5, 12.3). What is the probability that the value of is
in this interval?[Review
Question]:The higher the level of confidence you
choose, the ____(more/less) sure you can be that mu will be in the confidence
interval. The _____(more/less) precise, or _____(wider/narrower) you interval
will be.
1. A shipment of 1000
small lab mice arrives at the animal care facility with the weight following a skewed distribution (.0/msohtmlclip1/01/clip_image010.gif”>. A sample of 40
mice is selected and weighed. The sample average weight is 10.2 g, and the
sample standard deviation is 2 g. a. What are the
population and sample in this question? b. Since we know the.0/msohtmlclip1/01/clip_image012.gif”>, we can compute the confidence interval with the Z-method. What is the
margin error? c. Compute and
interpret a 90% confidence interval
for the mean weight of all the mice in the shipment. 2. What critical value t* would you use for a confidence interval for
the mean of the population in each of the following situations? a. A 95% confidence interval based on n=10 observations.b. A 99% confidence interval from an simple random sample of 20
observations.c. An 80% confidence interval from a sample of size 73.
A student in wildlife management
studied trout habitat in the upper Shavers Fork watershed in West Virginia. The
springtime water pH of 29 randomly selected tributary sample sites was found to
have the following values:6.0/msohtmlclip1/01/clip_image013.gif” alt=”http://ebooks.bfwpub.com/psls3e/tables/17_T_UN_4.gif”>a.
What is the standard error of the mean.b.
Use a 90% confidence interval to
estimate the mean springtime water pH of the tributary water basin around the
Shavers Fork watershed4. A dendritic tree is a branched structure that
emanates from the body of a nerve cell. In a study of brain development,
researchers examined brain tissue from 36 adult guinea pigs. The investigators
randomly selected nerve cells from a certain region of the brain and counted
the number of dendritic branch segments emanating from each selected cell. A
total of 36 cells (1 per pig) was selected, and the resulting counts were as
follows:measurement282438254226294525264928354726313528414633242632483535395338385917264453a) Construct a 95% confidence interval for the
population mean of dendrite branch segments (The variable can be seen as
continuous in this case). b)
Suppose
you want to estimate the population mean to be within 2 cells, how many pigs
should be examed? 7[OQ]
Create a confidence interval
problem and specify why you should use
the Z-method or T-method. Provide solution
to your question and attach your data set.