Final Exam Review Questions

Math 366 Exam Three Review Questions

There are 16 movies with a "PG-13" rating and 15 movies with an "R" rating. How do these two groups compare with respect to average gross earnings (is there evidence that the average gross earnings from each type is equal)? Consider the following Minitab output.
```
Two Sample T-Test and Confidence Interval

Two sample T for average gross earnings
R=1,PG-13=2  N      Mean     StDev   SE Mean
1           15      82.1      47.3      12.2
2           16     172.0     150.3      37.6

95% CI for mu (1) - mu (2): ( -172.9,  -6.9)
T-Test mu (1) = mu (2) (vs not =): T = -2.214  P = 0.0348  DF = 29
Both use Pooled StDev =  112.98
```
1. What is the hypothesis?
2. What is the test statistic and the degrees of freedom?
3. What is the p-value?
4. What is the conclusion?
5. What is the 95% Confidence Interval?
To compare the age at first marriage of females in two ethnic group A and B, a random sample of 100 ever-married females in taken from each group and the ages at first marriage are recorded. Suppose that 100 females sampled from each group are asked the question: "did you get married before you were 19?" and that the following responses are obtained:
```
	Chi-Square Test

Expected counts are printed below observed counts

             Ethnic Group
1=Yes, 2=No  A        B    Total
    1       62       29       91
         45.50    45.50

    2       38       71      109
         54.50    54.50

Total      100      100      200

Chi-Sq =  5.984 +  5.984 +
          4.995 +  4.995 = 21.958
DF = 1, P-Value = 0.000
```
1. What is the hypothesis?
2. What is the test statistic and degrees of freedom?
3. What is the p-value?
4. What is the conclusion?
An antibiotic for pneumonia was injected into 100 patients with kidney malfunctions (called uremic patients) and into 100 patients with no kidney malfunctions (called normal patients). Some allergic reaction developed in 38 of uremic patients and in 21 of the normal patients.
1. State the null and alternative Hypothesis.
2. Using an alpha = 0.05, is there evidence that the rate of incidence of allergic reaction to the antibiotic is higher in uremic patients than in normal patients?
3. Construct a 95% confidence interval for the difference between the population proportions.
One hundred draws are made at random with replacement from a box. The average on the draws is 102.7, and their SD is 10. Someone claims that the average of the box equals 100. Is this plausible? Assume the significance level is 5 percent.
1. What is the hypothesis?
2. What is the test statistic?
3. What is the p-value?
4. What is the conclusion?
5. What is the 95 percent of confidence interval?
Regression analysis (refer to study guide 2).
Compute average, SD, RMS, variance, median from a list (refer to study guide 1).
if p-value is less than alpha, do you reject the null hypothesis?
What is definition of the chi-square?
A safety study found that 99 of 150 males wore seatbelts and 146 of 200 women wore seatbelts.
1. What is the hypothesis statement?
2. What is the test statistic?
3. What is the p-value?
4. What is the conclusion?
5. Find the 95 percent confidence interval.
What is a 95 percent confidence interval for x = 105 and n = 500?
Is the chi-square test used for categorical or quantitative variables?
if sample size (n) is greater than or equal to 30, do you use a Z test statistic or t test statistic?
Given the following data set: 8, 12, 7, 19, 14, 9, what is the range?
Give a 95 percent confidence interval for a sample with an average of 12 and and SD of 20 when the sample size is 100.
Which values of the correlation coefficient (r) show the strongest relationship between two variables?
Given the following box of numbers { 1, 0, 1, 0, 1, 1 }. What is the the SD of this box?
What is the chance that an observed value of 75 will come from a data set of numbers having a average of 64 and a SD of 8?
Given x = 18 and n = 25, assume to proportion p = 0.5, (from text page 489 #11).
1. What is the hypothesis?
2. What is the test statistic?
3. What is the p-value?
4. What is your conclusion?
Exercise #1 on page 9.7 of coursepack.
Example on page 10.4 of coursepack.
What is the degrees of freedom for a r x c contingency table?
Given the following 2x2 contingency table:
```
	
        F   NF
    <50 7	8 
    >50 16	7
    
	
```
1. What are the expected values for this contingency table?
2. What is the test statistic?
3. What is the p-value?
4. Using alpha = 0.05, what is your conclusion about the relationship?
Given the hypothesis: Ho: mu <= 75 and H1: mu > 75 and the observed average = 78 and SD = 8, answer the following questions:
1. What is the definition and value of SD+?
2. What is the standard error (SE of the average)?
3. What is the test statistic?
4. What is the p-value?
5. What is the conclusion?
What is the definition of RMS?
In a quality control study that looks for the percentage of water in a tetrahydra floruine still, what is the null hypothesis? Hint: water is the still causes and explosion.
What is the equation for degrees of freedom for a one category chi-square problem?
A company offers an unconditional guarantee on its product for one year. It wants to study the issue of whether product failures are due to customers using the product improperly. Did they read the directions on the proper use of the product? To collect information they found in their records 100 customers who had returned the product due to its failure. Of these people, they found that 40 had read the directions and 60 had not. Realizing that a control group was needed they selected a sample of 5000 of their customers who had not had product failure. Among these people they found that 500 had read the directions and 4500 had not. They were puzzled to note that 500 out of 5000 is lower than 40 out of 100 -- apparently its better not to read the directions!
1. What is the risk product failure for those who read the directions vs those who did not?
2. What is the relative risk?
3. What is the odds and the odds ratio for product failure for those who read the directions vs those who did not?

Answers: