# Mathematics

Project 3 (Statistical Inference)

Due date: Sunday, December 8, 2013 by 11:59 PM EST

Total points possible: 75

This project may be turned in via Oncourse Assignments or at my office

(Hayes 255-R). If I am not there, place it under the door.

Students can work individually or in groups. Group work is encouraged.

The maximum group size allowed is three (3).

If working in groups, each group member must contribute to the project.

If working in groups, please turn in only one (1) completed project file.

If working in groups, please clearly list all group members.

The work needs to be clear and well organized. Points will be deducted for

work that is not clear or missing.

Clearly label each part of the project.

Note, you can use Excel, Word, or do the project by paper and pencil / pen.

Work done by paper and pencil/pen can then be scanned if you are submitting

the project via Oncourse Assignments. I will also take paper copies at my

office.

You must show your work for the calculations. Simply providing an

answer is not enough for the calculations. Please see the grading rubric for

more information.

All the data for the project can be found in the Excel file: Project3_Data.

There are two worksheets in this Excel file. See the case below for

information regarding the data.

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Note, this case study and project are the property of Dr. Marcy Jance

(your instructor). Under no circumstances is this case study or project to

be posted to any online web site or used outside of this class without the

permission of Marcy Jance.

The Bakery

By Dr. Marcy Jance

CASE 3: STATISTICAL INFERENCE

Emily has recently taken over her grandparent’s bakery business. She is

learning the new business and wants to continue the past success of the bakery

which has been in her family for over fifty years. Currently, the bakery’s primary

products are bread, cakes, cookies, cupcakes, doughnuts, muffins, pies, and rolls.

Emily is curious to see what the average daily sales are at her store. She

believes that it is around $1550. Emily collects data from the past 100 days.

Table 1 in the Project3_Data Excel file contains the total daily sales for the past

100 days. Assume this data comes from a normally distributed population

where the population standard deviation is unknown.

In addition, Emily is wondering whether she should add additional breakfast

items such as French toast and egg sandwiches. There are many businesses in the

downtown area near her bakery so this may provide quick breakfast solutions for

people on their way to work. She believes that 40% of her customers will

definitely purchase breakfast items (Yes response). Emily asks 300 customers

whether they would purchase breakfast items if they are available. Table 2 in the

Project3_Data Excel file provides the customer responses of Yes, No, and Maybe.

Now that Emily has all this data she would like some help with the

following:

1) Construct 90%, 95%, and 99% confidence intervals for the population mean of total daily sales.

2) Run a hypothesis test on the population mean for total daily sales. Use a hypothesized value of $1550 and test at levels of significance of 0.01, 0.05,

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and 0.10. Use both the critical value and p-value approaches when testing

at each level of significance.

3) Run another hypothesis test on what you believe is the true average total daily sales at the bakery. Test at levels of significance of 0.01, 0.05, and

0.10. Use the critical value and p-value approaches when testing at each

level of significance.

4) Construct 90%, 95%, and 99% confidence intervals for the population proportion of those that will definitely purchase breakfast items (Yes

response).

5) Run a hypothesis test on the population proportion of those that will definitely purchase breakfast items (Yes response). Use a hypothesized

value of 0.40 and test at levels of significance of 0.01, 0.05, and 0.10. Use

both the critical value and p-value approaches when testing at each level of

significance.

6) Run a hypothesis test on what you believe is the true proportion of people who will definitely purchase breakfast items (Yes response). Test at levels

of significance of 0.01, 0.05, and 0.10. Use the critical value and p-value

approaches when testing at each level of significance.

Finally, Emily would like her report to include observations and

recommendations based on the results of the confidence intervals and hypothesis

tests for the population mean and population proportion.

Grading Rubric:

Six (6) Confidence Intervals:

o Each confidence interval is worth 4 points.

o 3.0 to 4.0 points: Both the upper and lower limits of the confidence

interval are correct or there is a minor error. In addition, work is

shown. Work shown means that more than just an answer was

provided. One has clearly shown how one constructed the confidence

interval. For example, formulas and calculations are shown.

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o 2.0 to under 3.0 points: A decent attempt; however, there are some

errors or little or no work was shown.

o 0.0 to under 2.0 points: Not attempted or major errors.

Four (4) Hypothesis Tests:

o You will run four hypothesis tests. Two hypothesis test for the

population mean and two for the population proportion.

o Make sure that your hypothesized value for the second hypothesis

test for the population mean is different from 1550 and not set to

the sample mean.

o Make sure that your hypothesized value for the second hypothesis

test for the population proportion is not the same as 0.40 and is

different from the sample proportion value.

o Each hypothesis test is worth 10 points.

o Each hypothesis test needs to include the following:

State the null and alternative hypotheses (1 point possible)

Calculate the test statistic (1 point possible)

Show the critical values (1 point possible)

Calculate the p-value (1 point possible)

Use the critical value approach and conclude whether one

should reject or not reject the null hypothesis. Clearly explain

why it is rejected or not rejected (3 points possible).

Use the p-value approach and conclude whether one should

reject or not reject the null hypothesis. Clearly explain why it is

rejected or not rejected (3 points possible).

Written Report:

o The report is worth 11 points and includes observations and

recommendations based on the results of the confidence intervals and

hypothesis tests for the population mean and population proportion.

o The report should be at least three paragraphs in length. A

paragraph includes at least three complete sentences. Watch your

grammar and spelling.

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o 9.0 to 11.0 points: The write-up is well written (few or no grammar and spelling issues), is at least three paragraphs in length, and includes

observations and recommendations based on the results of the

confidence intervals and hypothesis tests for the population mean and

population proportion. Your statements are accurate or very few

minor mistakes.

o 6.0 to under 9.0 points: A decent attempt at the write-up. However, there may be some grammar, spelling, and/or length issues, or

mistakes/inaccuracies in one’s statements.

o 0.0 to under 6.0 points: Has not attempted or has not made a decent attempt at the report. The report does not sufficiently provide

observations and/or recommendations that are based on the results of

the confidence intervals and hypothesis tests. Also it is possible that

there may be serious grammar, spelling, and/or length issues with the

report.