Researchers investigated the relationship between caffeine consumption and happiness. The participants in this study were asked to abstain from drinking coffee for two months and were then given a happiness assessment which was graded on a scale of 0 (unhappy) to 5 (happiest). Then they were told to drink 4 or more cups of coffee each day for 2 months and were administered the same happiness assessment. The researchers constructed a 99% confidence interval for the mean difference in happiness scores (with coffee minus without coffee) was between 0.3 and 2.1. The researchers concluded that drinking 4 or more cups of coffee each day makes one happier. This is a reasonable conclusion because values in the interval are . Therefore, the difference between happiness with coffee and without coffee is likely , and hence, happiness with coffee is , on average