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statistical concept

Project #2 – MAT 151

This is an individual project.

Answer the following questions in complete sentences and in your own words. Please show your work this time on how you get numerical answers. List out each step that you did in detail. The weight of the project is equivalent to a test grade.

Please put a page break between answers for each section of questions.

The answers for each question will use the following rubric for grading purposes.

10 Points

7 Points

4 points

1 Point

Understood concept and wrote a coherent and appropriate answer with enough detail.

AND

Showed work and correct numerical answer

AND

No spelling errors.

Not a full explanation of statistical concept, had the basic idea, but not enough detail in the answer.

OR

Right numerical answer, but didn’t show work on how they got the answer.

OR

Spelling errors.

Wrote an incoherent and not complete answer without enough detail.

AND

Wrong numerical answer and didn’t show work.

AND

Spelling errors.

Right numerical answer, but:

No sentences,

No explanation of answer,

No meaning behind the numbers.

Section #1

Suppose your class is investigating the weights of Snickers 1-ounce fun-size candy bars to see if customers are getting full value for their money. Assume that the weights are normally distributed with a population standard deviation s = 0.005 ounces. Several candy bars are randomly selected and weighed with sensitive balances borrowed from the physics lab. The weights are:

0.95

1.02

0.98

0.97

1.05

1.01

0.98

1.00

Ounces. We want to determine a 90% confidence interval for the true mean, µ.

1. What is the sample mean?

2. Explain the meaning of the confidence interval.

3. Determine the z-value. Explain in detail how you knew to use a z-value for this question?

4. Find the margin of error.

5. Determine the 90% confidence interval for the mean weight of the candy bars.

Section #2

The composition of the earth’s atmosphere may have changed over time. One attempt to discover the nature of the atmosphere long ago studies the gas trapped in bubbles inside ancient amber. Amber is tree resin that has hardened and been trapped in rocks. The gas in bubbles within amber should be a sample of the atmosphere at the time the amber was formed. Measurement on specimens of amber from the late Cretaceous era (75 to 95 million years ago) gives these percents of nitrogen:

63.4

65.0

64.4

63.3

54.8

64.5

60.8

49.1

51.0

These values are quite different from the present 78.1% of nitrogen in the atmosphere today, but are these differences significant? Assume (this is not yet agreed on by experts) that these observations are an SRS from the Cretaceous atmosphere and the distribution of gas with an approximately normal distribution.

1. Describe the population of interest and the parameter you want to draw conclusions about.

2. Graph the data and comment on skewness and outliers. Can the t procedures be used in this situation?

3. What is the critical t-value for a 95% confidence interval? What are the degrees of freedom that you used to find the t-value.

4. Construct a 95% confidence interval gfotr the mean percent of nitrogen in ancient age.

5. Interpret this confidence interval.