Part 1 - Homework Assignment
1. Determine whether the samples are independent or dependent.
The effectiveness of a new headache medicine is tested by measuring the amount of time beforethe headache is cured for patients who use the medicine and another group of patients who use aplacebo drug. Explain.
2. Determine whether the samples are independent or dependent.
The effectiveness of a headache medicine is tested by measuring the intensity of a headache inpatients before and after drug treatment. The data consist of before and after intensities for eachpatient.Explain.
3. In a random sample of 500 people aged 20-24, 22% were smokers. In a random sample of 450people aged 25-29, 14% were smokers. Test the claim that the proportion of smokers in the twoage groups is the same. Use a significance level of 0.01.Show all steps of the hypothesis test and all calculations.
4. A researcher wishes to determine whether people with high blood pressure can reduce theirblood pressure by following a particular diet. Use the sample data below to construct a 99%confidence interval for µ1 - µ2 where µ1 and µ2 represent the mean for the treatment group andthe control group respectively.
Show all steps of the hypothesis test and all calculations. Use the following t-distribution table -
https://www.itl.nist.gov/div898/handbook/eda/section3/eda3672.htm
For questions 5 - 9 below, use the traditional method of hypothesis testing to test the given claim about the means of two populations. Assume that two dependent samples have been randomly selected from normally distributed populations.
Five students took a math test before and after tutoring. Their scores were as follows.
|
Student
|
A
|
B
|
C
|
D
|
E
|
|
Before
|
71
|
66
|
67
|
77
|
75
|
|
After
|
75
|
75
|
65
|
80
|
87
|
Using a 0.01 level of significance, test the claim that the tutoring has an effect on the math scores.
5. State the null and alternative hypotheses.
6. Find d, d-, and sd,
7. Find the value of the test statistic, t.
8. Find the critical value(s) and state the decision about the null hypothesis.
9. State the conclusion in non-technical terms.
Part 2 - Homework Assignment
The paired data below consists of test scores and hours of preparation for 5 randomly selected students. Use this data set to answer the questions below:
x Hours of preparation 5 2 9 6 10
y Test score 64 48 72 73 80
1. Use the given data to find thecorrelation coefficient r, regression equation and scatter plot in MS Excel.
2. Based on the linear correlation coefficient r, is this a good model? Explain.
3. What is the best predicted test score for a student who spent 7 hours preparing for the test?
4. Find the standard error. Use formula or MS Excel.
5. Find the 99% prediction interval for the test score of a person who spent 7 hours preparing for the test.
6. Find the explained variation.
7. Find the unexplained variation.
8. Find the total variation.
9. Find the value of r2 and explain its meaning.
10. If the data point ( 3, 100) is added to the data set, how would this effect the results of the regression analysis? Is this data point an outlier, influential point or both? Explain.
Part 3 - Homework Assignment
An investigator analyzed the leading digits of the amounts from 200 checks issued by three suspect companies. The frequencies were found to be 68, 40, 18, 19, 8, 20, 6, 9, 12 and those digits correspond to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively. If the observed frequencies are substantially different from the frequencies expected with Benford's law, the check amounts appear to be the result of fraud. Use a 0.05 significance level to test for goodness-of-fit with Benford's law.
1. Calculate the X2 test statistic.
2. Calculate the X2 critical value.
3. Is there sufficient evidence to conclude that the checks are the result of fraud?
Alert nurses at the Veteran's Affairs Medical Center in Northampton, Massachusetts, noticed an unusually high number of deaths at times when another nurse, Kristen Gilbert, was working. Kristen Gilbert was arrested and charged with four counts of murder and two counts of attempted murder. When seeking a grand jury indictment, prosecutors provided a key piece of evidence consisting of the table below. Use a 0.01 significance level to test the defense claim that deaths on shifts are independent of whether Gilbert was working.
|
|
Shifts With a Death
|
Shifts Without a Death
|
|
Gilbert Was Working
|
40
|
217
|
|
Gilbert Was Not Working
|
34
|
1350
|
4. Calculate the X2 test statistic.
5. Calculate the X2 critical value.
6. Is there sufficient evidence to reject the defense claim that deaths on shifts are independent of whether Gilbert was working?