Statistics

Jager Name__________________________

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Data Analysis #3

ST314 Total: 40 points

Due: Monday July 18th, at 11:59pm PST • Material from Week 4 Course Notes and Chapters 7 and 8 are covered on this analysis. • R code and Datasets can be found in the Data Analysis #3 Instructions • Please download, complete and upload as PDF or Word Document. - No other format will be accepted. • Please upload all pages as one file. • Typing or entering answers by hand is accepted as long as solutions are neatly given and document is

uploaded as PDF. Okay if “scanned” with phone however must be PDF. • Give the solutions in the space provided, add more pages as needed. • After submission, please review your submission to ensure correct document has been uploaded. • Working with others is encouraged, however, final work should be your own. Duplicate assignments

will be considered a violation of academic dishonesty.

Jager Name__________________________

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Part I (4 points) Perform a hypothesis for the null and alternative hypotheses: 𝑯𝑯𝟎𝟎: 𝝁𝝁 = 𝟓𝟓 𝑯𝑯𝒂𝒂: 𝝁𝝁 < 𝟓𝟓

The following is the sample information. 𝒙𝒙� = 𝟒𝟒. 𝟓𝟓 𝒔𝒔 = 𝟏𝟏. 𝟐𝟐 𝒏𝒏 = 𝟏𝟏𝟏𝟏 𝜶𝜶 = 𝟎𝟎. 𝟎𝟎𝟓𝟓

a. (1 point) Calculate the test statistic, p-value and give a general conclusion of reject or fail to reject based

on the significance level.

b. (1 point) Now suppose you know 𝜎𝜎 = 1.2. Calculate the test statistic, p-value and give a general conclusion of reject or fail to reject based on the significance level.

c. (2 points) What is the same and what is different between a and b? Why? Be specific.

Jager Name__________________________

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Part II (6 points) What type of test is it? Match the scenarios with the type of procedure that should be used. Include why you believe that to be the best procedure. A. One sample z test for a mean B. One sample z test for proportions C. One sample t test Scenario 1. A construction engineer would like to test whether a large batch of pressure treated lumber boards are acceptable for use by a given manufacturer. The boards are advertised as 4”x4”x16’ and should weigh 77 lbs. For the boards to be acceptable there should be no evidence that the boards weigh other than 77 lbs on average. The engineer takes a random sample of 30 boards and finds the average of the sample to be 76.8lbs with a sample standard deviation of 0.16 lbs. What type of variable is described in this scenario? What type of test is appropriate for this scenario? Scenario 2. An engineer has designed a soft serve ice cream machine that dispenses a certain serving size of ice cream by the push of a button. The amount of ice cream inevitably varies a bit from serving to serving. The engineer would like to test whether the machine is serving the correct weight on average. Suppose the engineer know that weight of all servings varies on average 0.09 ounces. To test whether the average weight differs significantly from 6.0 ounces, the engineer samples of 6 ice cream servings. The sample yielded an average of 6.01 ounces. What type of variable is described in this scenario? What type of procedure is appropriate for this scenario and why?

Scenario 3. The managers at a customer service call center would like to monitor whether their employees are suggesting an upgrade to customers when on a call. It is not possible to listen to every call. They randomly sample 200 calls and record whether or not an upgrade was suggested. They understand that it is not possible to suggest an upgrade on every call, so they assume that 10% of calls will not be suggested an upgrade. However, if data suggests there is evidence more than 10% of service reps did not offer an upgrade, the managers plan to further investigate each service rep and their individual calls. What type of variable is described in this scenario? What type of procedure is appropriate for this scenario and why?

Jager Name__________________________

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Part III (17 points) The data provided in this analysis was obtain from the USDA.gov website and is a compilation of information provided from the US Census Bureau. The NoHSEducation.csv data file contains the reported percent of the adult population that have less than a high school diploma nor a GED for the years 1990, 2000 and 2014. The observational unit is geographical areas in the US, which are most often state counties but also include Washington DC and locations in Puerto Rico. Counties or locations with missing data have been omitted. From this information, and the R code provided in the instructions, please answer the following questions. Note: If you would like to view the full data set you can at http://www.ers.usda.gov/data-products/county-level-data-sets/download-data.aspx under Educational attainment for the U.S., States, and counties, 1970-2014. Also see documentation if interested.

a. (3 points) We would like to look at the difference in percentages among adults with less than a high school diploma for 2000 and 2014. Create a histogram of the differences. Include and describe the plot using terminology we learned in week 1.

b. (1 points) Provide a table that includes the mean, standard deviation and sample size.

Suppose we want to test whether, among the selected geographical regions, the percent of adults without a high school diploma has decreased from 2000 to 2014, on average. In other words, we want to test whether the average difference is greater than zero. Perform an analysis. Use a significance level of 0.05.

c. (1 points) State the null and alternative hypothesis to answer the question of interest. d. (3 points) Calculate the test statistic by hand and obtain a p-value by table. Show work. e. (3 points) Calculate the 95% Confidence Interval by hand. Show work. f. (2 points) Obtain a p-value from a t test and confidence interval using R. Paste your output. Are your

answers the same/similar as by hand? g. (4 points) Using the R output (from f.) give a four part conclusion (shown in notes) and thoroughly

answer the question of interest. Must include context. h. Optional: Perform the same test on the difference between 1990 and 2014. Did your results change?

Jager Name__________________________

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Part IV. (15 points) According to a Gallup Poll conducted from June 2 – 7th, 2015 92% of voters in the US would vote for a women president. See poll and info: http://www.gallup.com/poll/183713/socialist-presidential- candidates-least-appealing.aspx Use ST314D Student Information Survey from our class to answer whether there is evidence the proportion of OSU engineering students that would vote for a women president is different than 92%. Use a significance level of 0.10. See the R Code in Data Sets and Code for more information.

a. (2 points) Include a barchart or table of the data. b. (1 point) State the null and alternative hypotheses. c. (2 points) We would like to use our class data to evaluate the proportion of all OSU engineering students

that would vote for a women president. Do you think this is reasonable why or why not? d. (1 points) Check sample size conditions. Are they met? If not, still proceed. e. (2 points) Calculate the test statistic. Show work! f. (1 points) Give the appropriate p-value and state whether it is one-sided or two-sided. g. (2 points) Calculate the appropriate 90% confidence interval. Show work! h. (4 points) Finally, using the results from parts e and f, summarize your conclusions to the university.

Interpret the CI and results of your test. Use the four part conclusion method. Include context!