Researchers at a medical center studied the amount of caffeine, in milligrams (mg), contained in a 16-ounce cup of coffee made at one machine at the center's cafeteria. They selected a random sample of 40 16-ounce cups of coffee made at different times of the day during a one month period. The mean and standard deviation of the amount of caffeine in the sample were 159.88 mg and 36.72 mg, respectively. A graph of the sample data revealed a right skew with one outlier. The researchers will construct a
confidence interval to estimate the amount of caffeine for all 16-ounce cups made at the machine.
Which of the following conditions is not needed for the inference?
А
The samples were selected at random.
B
The observations are independent of one another.
The sample size of 40 is less than 10% of the population size.
D
The graph of the sample data is symmetric with no outliers.
E
The sample size is large enough to assume that the sampling distribution of sample means is approximately normal​