Some people are concerned that new tougher standards and high stakes
tests adopted in many states may drive up the dropout rate. The National
Center for Education Statistics reported that the high school dropout rate
for the year 2000 was 10.9%. One school district, whose dropout rate has
always been very close to the national average, reports that 210 of their
1782 students dropped out last year. Use this sample data and a 0.05
significance level to test the claim that the national high school dropout
rate is now greater than 10.9%.
Show all the steps of your hypothesis test including a) the claim being tested, b)
the null and alternative hypothesis, c) the test statistic, d) the p value, e) initial
conclusion, and f) a final conclusion about the original claim.
2. A diet guide claims that you will get 120 calories in a serving of vanilla
yogurt. Consumer Reports tested 14 brands of vanilla yogurt and found
the following numbers of calories per serving:
160 200 220 230 120 180 140
130 170 190 80 120 100 170
Test the claim that the mean number of calories per serving of vanilla
yogurt is 120. Use a significance level of 0.05.
Show all the steps of your hypothesis test including a) the claim being tested, b)
the null and alternative hypothesis, c) the test statistic, d) the p value, e) initial
conclusion, and f) a final conclusion about the original claim. Since this was a
small sample, what assumption do we have to make about our population in
order to conduct this test with one of the methods from Chapter 8?
3. Samples of body temperatures were collected for a group of women and a
group of men. The summary statistics are given below:
Women:
n1 = 15 sample mean = 98.38 ˚F s1 = 0.45 ˚F
Men:
n2= 91 sample mean= 98.17 ˚F s2 = 0.65 ˚F
a. Use a 0.01 significance level to test the claim that women and men
have different mean body temperatures using the p value method.
Show all the steps of your hypothesis test including a) the claim being
tested, b) the null and alternative hypothesis, c) the test statistic, d) the
p value, e) initial conclusion, and f) a final conclusion about the original
claim.
b. Build a 99% confidence interval for the difference between the mean
body temperatures of women and men.
c. Do the hypothesis test and the confidence interval lead you to the
same conclusion about the two means?
How do you know that the confidence interval leads you to the same
conclusion as the hypothesis test?