# Statistic project

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, do the project by paper and pencil / pen, or a combination (e.g. Excel and by paper/pencil).  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.
Project Scenario  A business is curious about the average daily sales at its store and whether its customers would like it to have Saturday hours from 8 AM to 2 PM.   The owner believes that average daily sales are \$3800 and that 55% of its existing customers will come to the store if it is open on Saturdays.    The business owner collects sales data over a period of 80 days and polls 300 of the store’s customers regarding whether they will come to the store if it is open on Saturdays.
Table 1 in the Project3_Data Excel file contains the total daily sales for the past 80 days. Assume this data comes from a normally distributed population where the population standard deviation is unknown.  Table 2 in the Project3_Data Excel file provides the customer responses of Yes and No for the survey.
Now that the business owner has all this data, the owner would like some help with the following:  1) Construct 95%, 98%, 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 \$3800 and test at levels of significance of 0.01, 0.02, and 0.05.    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 business.  Test at levels of significance of 0.01, 0.02, and 0.05.    Use both the critical value and p-value approaches when testing at each level of significance.  (Note, do not use the sample mean as your hypothesized value or 3800 again!)  4) Construct 95%, 98%, and 99% confidence intervals for the population proportion of the store’s customers that will come to the store if it is open on Saturdays.  (Yes response).   5) Run a hypothesis test on the population proportion of the store’s customers that will come to the store if it is open on Saturdays (Yes response). Use a hypothesized value of 0.55

and test at levels of significance of 0.01, 0.02, and 0.05.  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 the store’s customers that will come to the store if it is open on Saturdays (Yes response).  Test at levels of significance of 0.01, 0.02, and 0.05.    Use both the critical value and p-value approaches when testing at each level of significance. (Note, do not use the sample proportion as your hypothesized value or 0.55 again!)
Finally, the business owner would like a report that includes 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.     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 3800 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 0.55 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. 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.

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EXCEL table 1

 3821 3738 4229 3846 2973 4140 4036 4027 3810 4380 3626 4404 4112 4041 4373 3274 4641 3836 3543 3800 4414 4886 3807 4246 3553 4120 4527 4060 4340 4239 4079 3981 4417 4526 3998 3632 3610 4192 4500 3754 4345 3866 3967 2978 3566 3629 5119 3092 4191 4556 4062 3922 4147 3328 4043 3936 4682 4024 3784 4155 3584 4261 3642 4441 3617 2851 4451 4226 3873 3947 4238 5658 2564 4531 3206 4172 3958 3935 3085 3740

EXCEL table 2

 Yes Yes Yes Yes Yes Yes No No No No No No No No No No Yes Yes Yes Yes Yes Yes Yes Yes Yes No No No No No No No No No No No No No No No No No No No No No No No No No No No Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No No No No No No No No No No No No No No No No No No No No No No No No Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes

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