The Centers for Disease Control (CDC) collects yearly statistics on drinking behavior in the United States by surveying a random sample of U.S. adults. The following data display the percent of adults aged 18 years and over who had 5 or more drinks in 1 day at least once in the given year.
Year Percent 95% confidence interval
1997 21.4 20.8-22.0
1998 20.2 19.6-20.8
1999 20.3 19.6-21.0
2000 19.2 18.6-19.9
2001 20.0 19.4-20.6
2002 19.9 19.2-20.5
2003 19.1 18.5-19.8
For which years (or year) above could you reject the null hypothesis that more than 20% of U.S. adults had 5 or more drinks in 1 day, at the .05 significance level?
There may be more than one correct answer.
To determine the years where you can reject the null hypothesis that more than 20% of U.S. adults had 5 or more drinks in 1 day at the 0.05 significance level, you need to compare the 95% confidence interval for each year to the value of 20%. If the confidence interval does not include 20%, you can reject the null hypothesis.
Let's calculate the confidence intervals for each year and compare them:
1. For the year 1997, the confidence interval is 20.8-22.0. Since 20% is not included in this interval, we can reject the null hypothesis for this year.
2. For the year 1998, the confidence interval is 19.6-20.8. Since 20% is included in this interval, we cannot reject the null hypothesis for this year.
3. For the year 1999, the confidence interval is 19.6-21.0. Since 20% is included in this interval, we cannot reject the null hypothesis for this year.
4. For the year 2000, the confidence interval is 18.6-19.9. Since 20% is included in this interval, we cannot reject the null hypothesis for this year.
5. For the year 2001, the confidence interval is 19.4-20.6. Since 20% is included in this interval, we cannot reject the null hypothesis for this year.
6. For the year 2002, the confidence interval is 19.2-20.5. Since 20% is included in this interval, we cannot reject the null hypothesis for this year.
7. For the year 2003, the confidence interval is 18.5-19.8. Since 20% is included in this interval, we cannot reject the null hypothesis for this year.
Based on these calculations, you can reject the null hypothesis for the year 1997. Therefore, the correct answer is: 1997.