Problems

A good approach to statistical analysis is to have an analysis plan in mind before you look at the data. What procedure would you use to analyze the following scenarios?

For complete credit, include

the name of the statistical test

the parameter being tested, value of the parameter and the signs of Ho

and Ha

Example What test would you use to determine whether the starting salaries for statisticians are greater than $80,000?

Ans. One-sample t-test for population mean Ho: =$80,000 vs. Ha: >$80,000

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1. About 9.3% of the adult American population has diabetes. Further research as indicated that this percentage may be higher in population with annual income of $35,000 or less. What procedure would you use to test whether this percentage is higher in a group with lower income?

2. A typical dental visit lasts around 60 minutes. Dental offices are experimenting with a new technology to clean teeth faster. What test would you use to determine if the new technology is working and saves time for both the office and patient?

3. The company that sells TurnItIn claims that their software lowers cheating and plagiarism in the universities that use it. College campuses indicate that about 10% of the students cheat when no monitoring software is used. What statistical procedure would you use to test whether the companys claim is effective for reducing plagiarism at =0.05?

4. According to gasbuddy.com the average price of gasoline in the Twin Cites last week was about $2.00/gallon. What statistical procedure would you use to test whether the price changed at the end of this week at =0.05?

5. About 90% of the University of Minnesota students think the university has an issue with crime on and near campus. In response to this, the university hired 15 additional police to patrol the campus during the night and early morning when most of the crimes occur. What statistical procedure would you use to test whether the additional police force is decreasing the percentage of students who think the university has a crime problem?

6. The University of Minnesota keeps crime statistics and reports an average of 0.75 crimes/month. What statistical procedure would you use to test whether the additional police force is decreasing the average number of crimes/month at =0.01?

7. In 2011, the average GRE score for the Quantitative Reasoning Section was 152. What statistical procedure would you use to test whether the average score for this section has changed since 2011 =0.01?

9.36 < you may assume that the data is drawn from a normal population.

1,Wine-pouring vending machines, previously available in Europe and international airports, have become popular in the last few years in the United States. They are even approved to dispense wine in some Wal-Mart stores. The available pouring options are a 5-ounce glass, a 2.5-ounce half-glass, and a 1-ounce taste. When the machine is in statistical control (see Exercise 7.42), the amount dispensed for a full glass is 5.1 ounces. Four observations are taken each day, to plot a daily mean over time on a control chart to check for irregularities. The most recent days observations were 5.05, 5.15, 4.95, and 5.11. Could the difference between the sample mean and the target value be due to random variation, or can you conclude that the true mean is now different from 5.1? Answer by showing the five steps of a significance test, making a decision using a 0.05 significance level

2,also assume that the machine dispenses wine in a random manner

9.46

refer to the previous exercise. when we test H0: M=0 against Ha: M>0, we get a p-value of 0.02

1. what would the decision be for a significance level of 0.05? interpret in context.
2. if the decision in part a is in error, what type of error is it?
3. suppose the significance level were instead 0.01. what decision would you make, and if it is in error, what type of error is it?

9.50

Detecting prostate cancer:Refer to the previous exercise about medical diagnoses. A

New York Times article (February 17, 1999) about the PSA blood test

for detecting prostate cancer stated: The test fails to detect prostate cancer in 1 in 4 men who have the disease.

a. For the PSA test, explain what a Type I error is, and explain the consequence to a

man of this type of error.

b. For the PSA test, what is a Type II error? What is the consequence to a man of this

type of error?

c. To which type of error does the probability of 1 in 4 refer?

r problem

Minnesotans rank high in getting a good night sleep according to the Center for Disease Control (CDC). They reported that 70.8% of the Minnesotans in their study got at least seven hours of sleep each night. Only South Dakota and Colorado report higher percentages, 71.6% and 71.5%, respectively. Follow the link below to read more about this finding-

http://www.kare11.com/news/study-minnesotans-rank-high-in-getting- good-sleep/48171655

Use the data collected in the Getting To Know You Survey to determine how University of Minnesota students compare to Minnesotans in general for the amount of sleep. This is a convenience sample, but for the purpose of this assignment you may assume that the students in the dataset where randomly selected. You can access the data using the following code, but remember that you will need to type this instead of copying and pasting it into R. Dont forget to attach() the dataset. Formatting of all R output can be preserved by changing the font of your output to Courier or Courier New.

NoU<-read.delim(http://stat.umn.edu/~bkuzmak/data/Getting2NoUS2016.txt, header=T)

attach(NoU)

2. Use t.test() to test whether students in Stat 3011 get an average of 7 hours of sleep per night during the week =0.05? Perform a 5-step test of hypothesis and interpret your results in the context of the problem.

3. Construct a 95% confidence interval for the average amount of sleep students get during the week. How do these results compare to the results of the statistical test performed in part 2 above? Explain.

4. It is believed that college students get more sleep on the weekend than during the week. Use the Getting To Know You Survey data to test the belief that students get more than 7 hours of sleep per night on the weekend at =0.05? Perform a 5-step test of hypothesis and interpret your results in the context of the problem.

this is code for R problem

NoU <- read.delim("http://stat.umn.edu/~bkuzmak/data/Getting2NoUS2016.txt", header=T)

attach(NoU)

#Number who get at least 7 hours of sleep

zzz.week.7<-ifelse(zzz.week<7,"No","Yes")

#Results

table(zzz.week.7)

#Total number of students in survey

length(zzz.week.7)