Individual Assignment 2

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Problem 1

According to research conducted by the fictional agency entitled Birth Rate and Health Outcomes, a sample of 3,500 women who gave birth reported that the sample mean age of first-time mothers in the U.S. was 24 years old with a sample median age of 21 and a sample standard deviation of 3.35.ⁱ

1. What is the point estimate of the population mean?

b. Statistically speaking, how would you define an unbiased estimator?

c. Based on the limited information presented, is this distribution likely to be skewed right, left, or normal? Explain.

d. Compute the 99% confidence interval of the population mean and interpret it.

e. Researchers hypothesize that the population mean age of first-time mothers is 23 years old. Will you reject or retain their hypothesis based on your work above? Explain.

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Problem 2

Consider a study that compares the Atkins diet to a conventional diet. A study at the University of Pennsylvania selected a sample of 63 subjects from the local population of obese adults. Researchers randomly assigned 33 to the Atkins diet and 30 subjects to a conventional diet. Test whether there is a significant difference in the mean weight loss (measured in pounds) across the two different diet programs.

Using software:

1. Generate summary statistics (central tendency and variability measures) for the two samples and briefly summarize what they say.

b. Conduct a test of significance for the difference between the mean sales across the two different locations in the store. Be sure to show the output from the software and interpret the results.

c. Construct a 95% confidence interval for the difference parameter in mean sales and make an interpretation.

d. Finally, are there any other factors, besides where the product is placed, that could possibly influence sales (identify at least 2)? Include a brief explanation of each.

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Problem 3: Hypothesis testing

For this problem, collect data on any variables of interest (sample size for each group of the two groups n=>30) and perform a two-sided significance test for comparing two independent population means. You can also simulate your own data.

Address the following:

1. A brief introductory paragraph describing the problem.
2. Set up your framework in a null and alternative hypothesis using symbols and notation as they are presented in the textbook.
3. A paragraph describing how you collected the data (i.e., the number of observations, time of day, etc. Please present the raw data in a table.
4. Create a graph of the means of the two samples using Excel. Clearly label your axes, and give your figure a title.
5. A section explaining the results of the analysis (calculated statistics, and p-values). Based on what you find, state your decision (whether you reject or fail to reject the H₀) and conclusion (whether you have sufficient or insufficient evidence for H₁).
6. Describe how would you change the experimental design to become dependent or related samples?

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Problem 4

This requires you to conduct a one-way analysis of variance.

Data are given to you on the “days on market” for a random sample of homes for sale by realtors using 5 different training programs that the realtors experienced. The 5 programs can be described as: computer-based course, campus training (on-site in a classroom), apprentice (work side-by-side with a mentor), field (solo field training), and self (a self-paced training course with books and coursework at home).

1. Present the null and alternative hypothesis for an experiment to determine if there are significant differences in the “days on market” for the realtors experiencing the different training programs.

1. Present the excel output for the one-way analysis of variance and state your decision (whether you reject or fail to reject the null) and conclusion (whether you have sufficient evidence for, or insufficient evidence for,….the alternative). Be sure to clearly state your F_computed (a.k.a. F-value) and P-value.

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Problem 5

Convert the following sales revenues figures into z-scores for 2 store locations where products are located: “front of the store” and “in the aisle of the store,” and identify which revenues are considered unusual according the approach “Z-Scores and Unusual Observations.” Please show your output (include a snapshot of your excel analysis with clear labels) and include a sentence or two on whether any are considered unusual.

Front of the store	Aisle of the store
113	132
114	134
105	119
125	167
98	129
106	115
147	130
116	152
102	134
128	121

You may assume that the population mean and population standard deviation are as follows:

Front of the store

? = 115

? = 15

Aisle of the store

? = 133

? = 16