07 Jan What is the exact mathematical

Week 4 discussion

MAT2058 Discussion Questions

Week 4

Text:

Textbook: Triola, M. F. (2014). Elementary statistics technology update (12th ed.). Boston, MA: Pearson Education.

Instructions:

• In the Course Home announcement area there should be a listing with your name and letter assigned for the discussion questions. If there is not such a list, then find the first letter of your last name below, and complete the two discussion problems associated with this letter.

• Please show all of the steps and processes you used to solve each of the problems.

• Remember to do both of the problems assigned and to respond to two of your classmates’ solutions.

• Please try to respond to two of your classmates who have had very different problems than yours assigned to them. You should receive more credit for doing so.

• In responding to the postings of at least two of your classmates, you can

o ask a question about your classmate’s solution(s)

o offer help when you see an error, or

o seek help in completing your own problems.

Remember that non-substantive posts such as “Good job!” will not count toward your participation score. Again, try to respond to at least two classmates who have problems assigned that are quite different from yours.

Please note that the assigned problems vary in difficulty and the list has been randomly generated for each of the two assigned problems.

Revised Week 4 A1 Discussion Questions

See the first instruction on

the previous page.

Please submit the two discussion items for your assigned letter.

Determine the value of the confidence

A If we wish to have a 95% confidence level, what would & coefficient z(?/2) for the situation below:

be the value of ??

1 ? ? = 0.95

If a population has a standard deviation ?

In the formula for the Margin of Error, E, what group of 5 units, what is the standard error of the

B of symbols represent E and what are the names of these & mean if samples of size 25 are selected?

symbols? Show all work.

In the formula for the Confidence Interval for the If a population has a standard deviation ?

C Mean, besides E, what group of symbol(s) represents & of 18.2 units, what is the standard error of

the Maximum Error of Estimate? the mean if samples of size 25 are

selected? Show all work.

A random sample of size 36 is to be

selected from a population that has a mean

? = 50 and a standard deviation ? of 10. –

A sampling distribution is a distribution of all sample

D statistics that describe a particular sample. T-F, and & – Find the mean of this sampling

why or why not? distribution.

– Find the standard error of this sampling

distribution.

Consider a sample mean (xbar) of 46

calculated from a sample of size 35 drawn

from a population of over 1000.

A confidence interval is an interval estimate of which: Would it be appropriate to use the standard

E a population parameter or a sample statistic? Please &

score table to look up the probability of a z

explain.

score calculated on these data? Why or

why not?

A random sample of size 36 is to be

The histograms of some sampling distributions are selected from a population that has a mean

F symmetrical. T-F What would make a histogram & ? = 50 and a standard deviation ? of 10.

symmetrical, and give an example of a symmetrical

distribution? Find the standard (z) score for a sample

value of 40.

If we wish to have a 98% confidence interval, what If a population has a standard deviation ?

of 25 units, what is the standard error of

G would be the value of ?/2? Show how you arrived at this &

the mean if samples of size 100 are

answer.

selected?

In the formula for the Confidence Interval

The mean of the sampling distribution of means is for the Mean, if the Confidence

H equal to the mean of the population. T-F, and why or & Coefficient, z(?/2) = 1.65, what is the

why not? Confidence Level?

I If we wish to have a 99% confidence interval, what & If a population has a standard deviation ?

would be the value of the confidence coefficient, of 25 units, what is the standard error of

z(?/2)? the mean if samples of size 36 are

selected?

The sampling distribution of sample means has a mean In the formula for the Confidence Interval

J equal to ? and a standard deviation equal to ?. T-F, and & for the Mean, if the Confidence

why or why not? Coefficient, z(?/2) = 2.58, what is the

Confidence Level?

An April 2004 article on Hear The

Issues.com stated that Americans have an

average of 2.24 televisions per household

(source: Nielsen Media Research). If the

If the Confidence Level is 99%, the Confidence standard deviation for the number of

K Coefficient for calculating the confidence interval for & televisions in a U.S. household is 1.2 and a

the mean is 2.33. T or F? Please show calculations as random sample of 80 American households

to why or why not. is selected, the mean of this sample

belongs to a sampling distribution.

– What is the mean and standard deviation

of this sampling distribution?

Determine the level of the confidence

The shape of the distribution of sample means is always given the confidence coefficient z(?/2) for

L that of an approximately normal distribution. T-F, Why & the following situation:

or why not?

z(?/2) = 2.58

Determine the level of the confidence

given the confidence coefficient z(?/2) for

The width of the Confidence Interval is inversely the following situation: z(?/2) = 1.96

M related to the Maximum Error of Estimate. T or F? &

Why or why not? Please show your work as to how you

obtain the confidence level from the given

confidence coefficient.

The standard error of the mean is the standard deviation What effect does the sample size have

upon:

N of the population from which the samples have been &

– the confidence interval

taken. T-F, and why or why not?

– the maximum error of measurement?

What differentiates a z test statistic for a population Consider a normal population with ? = 43

O from the z statistic for a sampling of means? Why the & and ? = 5.2. Calculate the z-score for an

difference? ?of 46.5 from a sample of size 16.

A recruiter estimates that if you are hired

to work for her company and you put in a

full week at the commissioned sales

representative position she is offering, you

will make “$525 plus or minus $250, 80%

of the time.” She adds, “It all depends on

P The standard error of the mean is the standard deviation & you!” If the $525 is the mean, state what

of the sample selected. T-F, and why or why not? the following figures stand for in terms of

the confidence interval around this mean.

– What does the “$525 plus or minus

$250” mean?

– What does the “80% of the time” mean?

If ? is the standard deviation of a population, what What is the mathematical relationship

would be the standard deviation of the sampling

Q & between the confidence level and the level

distribution of sample means for samples of size n?

of significance, ??

Is there another name for this term?

The maximum error of estimate is a function of three

R factors: the level of confidence, sample size and & Explain the difference between a point

standard deviation. T-F, and why or why not? estimate and an interval estimate.

Consider a sample mean (xbar) of 46

calculated from a sample of size 51 drawn

If we wish to have a 95% confidence interval, what from a population of over 1000.

S & Would it be appropriate to use the standard

would be the value of the confidence coefficient?

score table to look up the probability of a

standard (z) score calculated on these data?

Why or why not?

What is the relationship between Sample Size and the Discuss the effect that the confidence level

T width of the Confidence Interval? Please explain &

has upon the confidence interval.

further as to why.

When calculating sample size for estimating population Determine the critical value, z(?/2), for the

U means, the sample size is controlled by three factors: & situation below:

level of confidence, maximum error of estimate, and

standard deviation. T-F, and why or why not? 1 ? ? = 0.90

In your own words, describe the

relationship between the following:

Which do you think you could place more confidence

V in: an interval estimate or a point estimate of a & – Sample size, sample standard deviation,

population mean, and why? and standard error.

The Maximum Error of Estimate is exactly equal to What is the relationship between ? and the

W half of the width of the confidence interval. T-F, and &

confidence level of a hypothesis test?

why or why not?

X Determine the level of confidence given the & If ? = 0.01, what is the confidence level of

confidence coefficient z(?/2) = 1.96. a statistical test?

In your own words, describe the

If we wish to have a 90% confidence interval, what relationship between the following:

Y would be the value of ?/2? Show how you arrived at & – Sample mean and point estimate

this answer.

What is the exact mathematical relationship between In your own words, describe the

relationship between the standard error and

Z the width of a confidence interval and the Maximum &

maximum error. You may use the

Error of Estimate?

formulas for each in your explanation.