Dentists believe that a diet low in sugary foods can reduce the number of cavities in children. Twenty children whose diets are believed to be high in sugar are examined and the mean number of cavities is 3.7 with a standard deviation of 0.4. Ten children whose diets are believed to be low in sugar are examined and the mean number of cavities is 3.6 with a standard deviation of 1.6. Construct a 99% confidence interval for the true difference between the mean numbers of cavities for children whose diets are high in sugar and those whose diets are low in sugar. Assume that the variances of the two populations are the same. Let Population 1 be children whose diets are believed to be high in sugar and Population 2 be children whose diets are believed to be low in sugar. Round the endpoints of the interval to one decimal place, if necessary.
Dentists believe that a diet low in sugary foods can reduce the number of cavities in children. Twenty children whose diets are believed to be high in sugar are examined and the mean number of cavities is 3.7 with a standard deviation of 0.4. Ten children whose diets are believed to be low in sugar are examined and the mean number of cavities is 3.6 with a standard deviation of 1.6. Construct a 99% confidence interval for the true difference between the mean numbers of cavities for children whose diets are high in sugar and those whose diets are low in sugar. Assume that the variances of the two populations are the same. Let Population 1 be children whose diets are believed to be high in sugar and Population 2 be children whose diets are believed to be low in sugar. Round the endpoints of the interval to one decimal place, if necessary.
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