project

OPTION 3: Confidence Interval on the Mean – one sample (T-Interval)

A) Introduction – introduce the topic and yourself: 5% of score

Explicitly identify the following:

1) Parameter of interest: __________________________

2) Population of interest (be as specific as necessary): ___________________________

3) Variable of interest: _____________________________

4) Then write a paragraph or two of introduction to your paper. In the paragraph, include at least the following information: Your research objective, your interest in the topic.

Describe in detail where you found your sample and specifically how you chose which individuals to survey.

B) Data Sets – Present your organized data and sample statistics: 15%

1) DATA SET A: a) Show the frequency distribution of your full data set. Call it Data Set A.

It must have at least 80 individuals: n > 80. You can use either a table or a histogram to show the distribution:

Identify b) sample size: __________ c) mean :___________ d ) standard deviation: ____________

e) Estimated Standard Error of the means (SE): ______________________. Round each to four decimal places if needed.

2) DATA SET B: Select some of the data points from Data Set A to create smaller data set. Call this Data Set B. It should have about half of the values from Data Set A.

a) Show the frequency distribution of Data Set B. You can use either a table or a histogram to show the distribution. USE THE SAME GROUPING (CLASSES) FOR EACH DATA SET:

Identify b) sample size: __________ c) mean :___________ d ) standard deviation: ____________

e) Estimated Standard Error of the means (SE): ______________________. Round each to four decimal places if needed.

f) Describe specifically how you chose the individuals from Data Set A to create Data Set B.

3) DATA SET C: Select between 10 and 20 data values from Data Set A to create a still smaller data set. Call this Data Set C.

a) Show the frequency distribution of Data Set C. You can use either a table or a histogram to show the distribution. USE THE SAME GROUPING (CLASSES) FOR EACH DATA SET

Identify b) sample size: __________ c) mean :___________ d ) standard deviation: ____________

e) Estimated Standard Error of the means (SE): ______________________. Round each to four decimal places if needed.

f) Describe specifically how you chose the individuals from Data Set A to create Data Set C.

C) The Intervals – Construct the Confidence Intervals for three different sample sizes and three different levels of confidence: 45%

1) Degrees of freedom (df) – determine the degrees of freedom for each Data Set.

Data Set A: df = __________ Data Set B: df = __________ Data Set C: df = __________

2) Choose three confidence levels, between 80% and 99%.

C-level 1: __________ C-level 2: __________ C-level 3: __________

3) Determine for each level of confidence you chose.

C-level 1: = __________ C-level 2: = __________ C-level 3: = __________

4) Critical Values – Each sample size together with a level of confidence will have a critical value.

a) Determine the critical values for each of the nine confidence intervals. Put the critical values in the chart below organized by either sample size or confidence level. Round each to three decimal places if needed.

b) To find the critical values, did you use the t-table or the calculator?

5) Show the formula for constructing confidence intervals for the mean by hand:

6) Confidence Intervals – Create a confidence interval for each of the three confidence levels for each of the three samples, for a total of nine confidence intervals. Put the intervals in the chart below. Round each to three decimal places if needed.

7) Determine the Margin of Error for each of the nine confidence intervals. Put the Margin of Errors in the chart below. Round each to three decimal places if needed.

8) Fill in the rest of the chart using values found in your results above.

n	df		s	SE	C-level	Critical value	Confidence Interval (CI)	E

Put the information in the chart organized by either sample size or confidence level for ease of comparison.

9) Interpret at least three of the confidence intervals in the context of the problem. Include population, parameter and variable.

D) Written Analysis – discuss validity and explain the results of your findings: 30%

1) Validity of the method

State the three requirements for valid inference on the mean using our methods

a) Population size:

b) Sampling Method:

c) Shape of the Sampling Distribution:

2) a) Estimate the population size for your population of interest. Explain your reasoning:

b) Verify whether the population size requirement is met (from 1a above) (Show your work):

3) Describe your sampling method (how you gathered the data) and explain if you think it might be biased or not. Explain whether or not this meets the requirement (from 1b above)

4) For Data Sets A and B, explain whether the shape of the sampling distribution requirement is met. Show your reasoning.

5) For Data Set C, a) display the boxplot and b) normal probability plot.

c) Explain why it is necessary to examine these graphs.

d) Interpret the graphs and tell whether the method is valid for your small data set (based on the graphs).

6) Effect of sampling and sample size

a) Identify which values from the confidence intervals (point estimate, standard error, critical value, etc.) were impacted by sample size and which ones weren’t, based on your observations.

b) Apply the Law of Large Numbers to your tests and explain which one of the three results should be most trusted.

E) Summary – summarize your results: 5% -

Write a paragraph summarizing your paper: Include: restate your research objective, an overall estimate of the parameter based on your findings, any possible flaws in your research (sampling method? sample size? population size?). Did the results concur for each sample? Why, why not? Note any interesting observations you had or possible extensions of this research.

x

x