Discuss the below:
Q1) UFO Sightings
Cases of UFO sightings are randomly selected and categorized according to month, with the result listed I the table below (based on the data from Larry Hatch). Use a 0.05 significance level to test the claim that UFO sighings occur in the different months with equal frequency. Is there any reasonable explanation for the two months that have the highest frequencies?
| Month |
Jan |
Feb |
March |
April |
May |
June |
July |
Aug |
Sept |
Oct |
Nov |
Dec. |
| Number |
1239 |
1111 |
1428 |
1276 |
1102 |
1225 |
2233 |
2012 |
1680 |
1994 |
1648 |
1125 |
Q2) M&M Candies
Mars, Inc. claims that its M&M plain candies are distributed with the following color percentages: 16% green, 20% orange, 14% yellow, 24% blue, 13% red, and 13% brown. Test the claim that the color distribution is as claimed by Mars, Inc. Use a 0.05 significance level.
Q3) Is Sentence Independent of Plea?
Many people believe that criminals who plead guilty tend to get lighter sentences than those who are convicted in trials. The accompanying table summarizes randomly selected sampe data for San Francisco defendants in burglary cases (based on data from "Does it Pay to Plead Guilty? Differential Sentencing and the Functioning of the Criminal Courts," by Brereton and Casper. Low and Society Review Vol. 16 No. 1). All the subjects had prior prison sentences. Use a 0.05 significance level to test the claim that the sentence (sent to the prison) is independent of the plea. If you were an attorney defending a guilty defendant, would these results suggest that you should encourage a guilty plea?
| |
|
Guilty Plea |
|
Not Guilty |
|
| Sent to Prison |
|
392 |
58 |
| Not Sent to Prison |
|
564 |
14 |
Q4) Clinical Trial of Lipitor
Lipitor is the trade name of the drug atorvastatin, which is used to reduce cholesterol in patients. Adverse reactions have been studied in clinical trials, and the table below summarizes results for infections in patients from different treatment groupls. Use 0.05 significance level to test the claim that getting an infection is independent of the treatment. Does the atorvastatin treatment appear to have an effect on infections?
| |
Placebo |
Atorvastatin 10mg |
|
Atorvastatin 40mg |
|
Atorvastatin 80mg |
|
| Infections |
27 |
89 |
8 |
7 |
| No Infection |
243 |
774 |
71 |
87 |
a) Why One Test?
Refer to the sample data given in Q1. If we want to test for equality of the three means, why don't we use three separate hypothesis for µ1=µ3?
| Data For Sample 1 |
400 B.C. |
131 |
138 |
125 |
129 |
132 |
135 |
132 |
134 |
138 |
|
|
1850 B.C. |
129 |
134 |
136 |
137 |
137 |
129 |
136 |
138 |
134 |
|
|
150 A.D. |
128 |
138 |
136 |
139 |
141 |
142 |
137 |
145 |
137 |
TRUE OR FALSE?
1. More variation should be expected between larger samples, which is apparent by the chi-square distribution.
2. A test of independence can be used to determine a cause-and-effect link between the variables being studied.
3. Using the F distribution for a one-way ANOVA, the degrees of freedom for the denominator will always exceed the degrees of freedom for the numerator.