project

OPTION 1: Hypothesis Testing on the Mean – one sample (T-Test)

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) 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) 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) 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 Tests – Perform the hypothesis Tests using the two approaches: 45%

Step 1 – a) Write a sentence making a claim. _________________________________

b) Explain how you decided on this claim.

c) Form the hypotheses using the symbol notation used in class.

Step 2 – Determine the level of significance and the rejection region

A) Describe a Type I Error generally speaking: _______________________________

Describe a Type I Error specific to this situation:

B) Describe a Type II Error generally speaking: _______________________________

Describe a Type II Error specific to this situation:

C) Tell any consequences (positive or negative) of making either type of error, and explain which error you think is worse, in this specific case.

D) Select your level of significance based on C) and explain why you chose the value you chose.

E) For each data set, determine the critical value(s) and identify the rejection region.

Data Set A: critical value(s) = __________ Data Set B: critical value(s) = __________

Data Set C: critical value(s) = __________

F) Draw a t-distribution for each sample size, showing the rejection region and critical value, clearly labeled

Step 3 – a) Show the formula for calculating the test statistic by hand:

b) Determine the value of the test statistic for each data set:

Data Set A: test statistic = __________ Data Set B: test statistic = __________

Data Set C: test statistic = __________

c) Show the probability notation for finding the P-value of the calculated test statistic specific to your research.

d) Determine the P-value for each data set:

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

e) In the t-distributions you drew above in Step 2– F, clearly indicate the locations of the test statistic and P-value.

f) Fill in the table using your results from above. Record your results in order of sample size. 

Round all calculated values to 4 decimal places if needed.

n	Observed value,	s	Standard Error, SE	Critical value(s)	Test statistic,	P-value

Step 4 – Use the Decision Rule to either reject or not reject the null hypothesis

Fill in the charts for each approach with the values from above and show the comparisons used to make your decisions.

P-Value Approach:

n		P-value	Compare P to	Decision (reject or do not reject H0)

Classical Approach

n	Critical Value(s) /Rejection Region	Test Statistic	Is t in rejection region?	Decision (reject or do not reject H0)

Step 5 – Write the conclusion - For each sample size, give the full conclusion in “plain English”, in the context of the problem.

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 hypothesis test (P-value, test statistic, critical value, etc.) were impacted by sample size and which ones weren’t, based on your observations in the test.

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, any possible flaws in your research (sampling method? sample size? population size?). Was the claim supported or not? Did the results concur for each sample? Why, why not? Note any interesting observations you had or possible extensions of this research.

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