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 the claim being tested: the null and alternative hypothesis: the test statistic: the p values:
Question #1
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
- the claim being tested:
- the null and alternative hypothesis:
- the test statistic:
- the p values:
- initial conclusion:
- a final conclusion about the original claim:
Question #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
- The claim being tested:
- The null and alternative hypothesis:
- The test statistic
- The p-value:
- Initial conclusion
- Final conclusion about the original claim
Question #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
1. 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
- the claim being tested:
- the null and alternative hypothesis:
- the test statistic:
- the p value:
- initial conclusion:
- a final conclusion about the original claim:
2. Build a 99% confidence interval for the difference between the mean body temperatures of women and men.
3. 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?
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