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?
Whatever year the percent was less than the maximum of the confidence interval of 20%, 2000 and 2003.
To determine which years we can reject the null hypothesis, we need to compare the confidence intervals to the percentage level mentioned (20%) and the significance level (0.05). The null hypothesis assumes that the true percentage of adults who had 5 or more drinks in 1 day is indeed 20% or more.
If the confidence interval does not include 20%, then we can reject the null hypothesis. In this case, since 20% is on the edge of the interval, we need to determine if it is included or not.
Let's analyze each year:
- 1997: The confidence interval is 20.8-22.0%. Since 20% is within this interval, we cannot reject the null hypothesis.
- 1998: The confidence interval is 19.6-20.8%. Again, 20% is inside this range, so we cannot reject the null hypothesis.
- 1999: The confidence interval is 19.6-21.0%. Once more, 20% is included, so we cannot reject the null hypothesis.
- 2000: The confidence interval is 18.6-19.9%. This time, 20% is outside the interval. We can reject the null hypothesis for the year 2000.
- 2001: The confidence interval is 19.4-20.6%. Here, 20% is within the interval, so we cannot reject the null hypothesis.
- 2002: The confidence interval is 19.2-20.5%. As before, 20% is included, so we cannot reject the null hypothesis.
- 2003: The confidence interval is 18.5-19.8%. Once again, 20% is inside this range, so we cannot reject the null hypothesis.
Based on these results, the only year for which we can reject the null hypothesis that more than 20% of U.S. adults had 5 or more drinks in 1 day is 2000.