# Stastistics

Further guidance for students on Integrative Project.

I would like you to think about a question that you can possibly answer with statistics and create an integrative project about it.  Here are some central questions to answer as you work through the project. I have broken it up into 19 question, please answer these on your integrative project.

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1. Identify a question you would like to answer using statistics which may be answered using a confidence interval in plain English.

Example:  What is the average GPA of an incoming student at MC

1. Identify the parameter related to your question and its symbol and its name.

Example:  m, mean

1. identify the statistic related to your question and its symbol

Example: x(bar), sample mean

III. List  your data(try to get at least 10 in your sample).

Example:  3.28, 2.41, 3.64, 1.28,3.56, 2.57, 3.10,2.94, 2.45, 3.16, 2.45

1. Describe your population of inteeest.

Example: All students at MC

Example:  11 Studens in my statistics class

1. Comment on how you obtained your sample

Example: Conducted an email survey of the students in my statistics class

• Comment on the bias in your sample

Example;  This sample is biased since it is only people in math 117, who need certain perquisites to take the course, this underrepresents students without the prerequisites.

• If there is bias in your sample comment on how you could have obtained an unbiased sample.

Example;  We could have gotten a numbered list of students at MC and chsen every 10th name on the list.

IX..   Find several confidence intervals using bootstrapping, what assumptions did you make?

Example:

95% (2.421,3.146)

99%: (2.315,3.231)

The assumption was made that the underlying distribution was approximately normal.

1. Create a question related to I, which may be answer with a hypothesis test

Example:  The average GPA for a student at MC is about 2.0

XII. Set up the hypothesis related to you question using the appropriate notation.

Example:

H0: m = 2.0  (the mean GPA is about 2.0)

Ha m ≠2.0  ( the mean GPS is different than 2.0)

XIII. Compute the value of the standardized test statistic to the nearest .01

Test statistic = =3.648

XIV. State the distribution and degrees of freedom if necessary.

T-distribution with 10 degrees of freedom, .00383

1. Find the p-value using a non-bootstrapping approach.

Examples:

.0083

XVI. Find the p-value using bootstrapping to the nearest .01

0

XVII.  Make a conclusion about the question you identified at the .05 level of significance.

Reject the claim that the mean GPA is 2.0 since the pvalue = .008<.05 = significance level.

XVIII  Identify the cases and variables.

Caes: students in survey, Variable: GPA

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