Math 116 – Group Quiz – Open books – 8.1-8.4Name______
SHOW ALL WORK on your paper. Make sure your group mate’s work is also perfect. I will grade both papers and your grade will be the lower of the two grades. NEATNESS REQUIRED! SHOW ALL WORK. By now you should know what I expect from you.
1) In your own words: Why do we construct confidence intervals?
2) Problem 12, page 421
Read the problem, and answer each of the following:
a) What is the population?
.
b) What is the variable? Include units.
c) What is the objective of the problem?
d) Explain how you use the calculator to obtain the sample mean and the sample standard deviation. Summarize please.
e) What is the point estimate?
f) Calculate the confidence interval. Remember that you have to show all work.
Write the answer:(……………… , …………………)
Write the answer in this form also ……………< µ < ……………….
g) Now check the answer with a feature of the calculator. Indicate feature used and results.
h) Complete the statement:
With ……..% confidence we can say that the cost of starting a candy franchise is
…………………. with a margin of error of…………………..
(How did you find the margin of error? Show it here: )
Finding sample size
i) Suppose you would like to have an estimate which is within 10,000 dollars of the true mean startup cost of a candy franchise. What should be the sample size selected in order to be 90% confident that the sample mean x-bar is within 10 thousand dollars of mu?
3) Read page 432 about how a Poll was conducted, and the guided exercise 5.
Part 1
a) Describe in words the population (Who was surveyed?)
b) What was the question asked?
c) What was the attribute considered a success?
d) What method of sampling was used? Stratified or Cluster?
e) Did we survey ALL US adults 18-year-old or older? If not, what part of this group was left out on this survey?
f) Is the sample selected representative of the population? Or is it biased?
3) Read page 432 about how a Poll was conducted, and the guided exercise 5.
Part 2
a) What is the sample size?
b) What is the point estimate?
c) What degree of confidence is being sought?
d) What is the margin of error given in the guided exercise 5?
e) What is the confidence interval? Write it in two ways.
f) With this confidence interval we are trying to estimate ……
g) With ……..% degree of confidence we can say that …..% of adults think that the democrats
would do a better job handling education, with a margin of error of………………..
h) Calculate the margin of error using the formula from section 8.3. Is it the same as stated in the guided exercise 5?
i) Use a feature of the calculator to calculate the confidence interval and check the results given in the guided exercise 5.
Sample size
a) What should be the size of the selected sample in order to be 95% confident that the estimate p-hat is within 1.5 percentage points of the true percentage p of all adults who will vote Democrat? Assume p-hat = .32 as stated in guided exercise 5.
This means the margin of error is at most …………….
b) Assume you have no information about p-hat. What should be the size of the selected sample in order to be 95% confident that the estimate p-hat is within 1.5 percentage points of the true percentage p of all adults who will vote Democrat?
c) Observe the results of (a) and (b). Why do you think statisticians prefer to use an estimate for p-hat if it is available from a previous study?
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