Question

4. The CDC publishes charts on Body Mass Index (BMI) percentiles for boys and girls of different ages. Based on the chart for girls, the mean BMI for 6-year-old girls is listed as 15.2 kg/m2. The data from which the CDC charts were developed is old and there is concern that the mean BMI for 6-year old girls has increased. The BMIs of a random sample of 30 6-year-old girls are given below.

24.5	16.3	15.7	20.6	15.3	14.5	14.7	15.7	14.4	13.2
16.3	15.9	16.3	13.5	15.5	14.3	13.7	14.3	13.7	16.0
14.2	17.3	19.5	22.8	16.4	15.4	18.2	13.9	17.6	15.5

a. State null and alternative hypotheses relevant to this situation.

b. Calculate the sample mean and standard deviation.

c. Since the sample size is relatively large, use s in place of σ and calculate the value of the z-test statistic. Then calculate the p-value.

d. Based on your answer to (c), do the sample data provide sufficient evidence that the mean BMI for 6-year-old girls has increased? Explain

Answer 1