Assignment 1 -
Problem 1 - The 2006 General Social Survey asked, "What do you think is the ideal number of children for a family to have?" the 1,097 females who responded had a median of 2, mean of 3.16, and a standard deviation of 1.91.
a. What is the point estimate of the population mean?
b. Find the standard error of the sample mean.
c. Compute the 95% confidence interval of the population mean and interpret it.
d. Is it plausible that the population mean could be equal to 2? Explain.
Problem 2 - Data are provided to you on pizza delivery times (in minutes) for 2 different classifications of stores: local and chain stores. The goal here is to determine whether there is a significant difference in the mean delivery time between the store classifications. Using software:
a. 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 delivery times of local and chain stores and (show the results) interpret the results.
c. Construct a 95% confidence interval of the difference between the two population mean delivery times and interpret it.
d. Finally, are there any other factors, besides the way the store is classified, that could possibly influence delivery times (try and list at least 2)? Include a brief explanation of each.
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:
a. A brief introductory paragraph describing the problem.
b. Set up your framework in a null and alternative hypothesis using symbols and notation as they are presented in the textbook.
c. A paragraph describing how you collected the data (i.e., the number of observations, time of day, etc. Please present the data in a table. Also, in this section, plot the means of the two samples using Excel.
d. 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).
e. Describe how would you change the experimental design to become dependent or related samples?
Problem 4 - This requires you to conduct a one-way analysis of variance.
Data are given to you about weights (pounds) of a random sample of professional football players on five teams. Conduct an appropriate test to determine if there are differences among the weights of the teams' football players. Present the results of the analysis and interpret them.
Assignment 2 -
Problem 1 - The 2014 Public Health Survey sampled 2,035 people and found an average systolic blood pressure reading (top #) of 134.65, a median of 119.56 and a standard deviation of 12.52.
a. What is the point estimate of the population mean?
b. Find the standard error of the sample mean.
c. Compute the 95% confidence interval of the population mean and interpret it.
d. Is it plausible that the population mean could be equal to 136? Explain.
Problem 2 - PepsiCo is analyzing whether there is a significant difference in the mean productivity between 2 shipping centers. Data are provided to you on the number of cases of soda (a measure of output) shipped per day for each of 2 shipping centers: shipping center 109 (a beautiful location that sits over a coastal town) and shipping center 111 (a busy operation located in a downtown area). The goal here is to determine whether there is a significant difference in the mean output levels across the 2 shipping centers.
a. 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 output levels and (show the results) interpret the results. Your set-up should look something like H0: µ109 = µ111 H1: since you're testing for a difference, think about which expression would work best here.
c. Construct a 95% confidence interval of the difference between the two mean output levels and interpret it. This is known as a confidence interval for a "difference parameter." Not exactly the same as what you did in Problem 1. With the interpretation, ask "does the interval contain zero?"
d. Finally, are there any other factors that could possibly influence productivity, as measured by output levels (try and list at least 2)? Include a brief explanation of each.
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:
a. A brief introductory paragraph describing the problem.
b. Set up your framework in a null and alternative hypothesis using symbols and notation as they are presented in the textbook. Should have the general set-up of H0: µ1 = µ2 H1: can have a <, or >, or ≠ depending on your question.
c. A paragraph describing how you collected the data (i.e., the number of observations, time of day, etc. Please present the data in a table. Also, in this section, please plot the means of the two samples using Excel.
d. 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).
e. Describe how would you change the experimental design to become dependent or related samples? Think about which factors you could possibly control for that weren't in the initial analysis.
Problem 4 - This requires you to conduct a one-way analysis of variance.
Data are given to you on the times to complete tax forms of a random sample of tax accountants using 3 different methods: face-to-face meeting, online meeting, and telephone meeting. Conduct an appropriate test to determine if there are differences among the times for the different methods. Present the results of the analysis and interpret them.
Attachment:- Assignment Files.rar