Quiz 6
1. A researcher wants to investigate the proportion of married men who are happy with their marriage to do this, he takes a sample of 100 men and finds that 72 reported being happy with their marriage. Should a confidence interval be constructed to determine the proportion of all men who are happy with their marriage? Why? (give a short explanation; 1-2 sentences)
2. Suppose a random sample of 64 cyclists on the Fred Meijer Heartland Trail was taken, of which 48 were wearing helmets. Find a 95% confidence interval for the proportion of all cyclists on the Fred Meijer Heartland Trail who wore helmets. Calculate the following quantities to lead you to the confidence interval.
a. Standard Error:
b. Margin of Error:
c. Critical Value:
d. Confidence Interval:
3. A study was made investigating student enrollment persistence with respect to hours worked per week. Students classified as Preserving (those who returned after the first semester of college) and non-persevering (those who did not return after their first semester of college) were asked about the work schedules during the first semester of college. From these students, the following data was collected.
If each group is considered a random sample, give a 95% confidence interval for average number of hours per week during the first semester of college for each group. Instead of answering the question posed, create a confidence interval for the difference in the average number of hours worked per week by persevering and non-persevering students. Calculate the following quantities to lead you to the confidence interval.
a. Standard Error:
b. Margin of Error:
c. Critical Value:
d. Confidence Interval:
e. Can you determine a difference in the average number of hours worked per week by persevering and non-persevering students?
f. If you answered yes to e, who works more? If you answered no to e, leave this blank.
4. On the first day of class, I gave you a survey. One question asked was how you would rank yourselves compared to others based on your IQ (1 is less than everyone else, 10 was higher than everyone else). I am interested in the average ranking WMU students give themselves based on their IQ. To determine this, I used a portion of our class' results. Below is the R output.
> IQ <- c(4, 8, 5, 10, 7, 6, 8, 8, 9, 9, 6, 8, 7, 6, 6, 7, 9, 8, 8, 8, 5, 7, 9, 8, 7, 5, 5, 6, 8, 9, 6, 4, 7, 5, 6, 6, 7, 6)
> t.test(IQ)
One Sample t-test
data: IQ
t = 28.1878, df = 37, p-value < 2.2e-16
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
6.423554 7.418551
sample estimates:
mean of x
6.921053
a. What is the confidence interval for this situation?
b. Interpret the confidence interval.