Question

The CDC publishes charts on Body Mass Index (BMI) for boys and girls of different ages. Based on the chart for girls, the mean BMI for 6-year-old girls is listed as 15.6 kg/m2. The data from which the CDC charts were developed is old and there is concern that the mean BMI for 6 year olds girls has increased. The BMI’s from a current random sample of 30 6-year-old girls is attached in a list on the next page. Use this data of current six year girls to test the claim that the mean BMI for current girls is greater than 15.6 (thus, testing that the mean BMI for six-year-old girls has increased). State the claim, null hypothesis, and alternate hypothesis in symbols. Claim: H_0: H_1: Copy and paste the sample of 30 BMI’s into stat crunch. Calculate the mean and standard deviation for the sample. x ̅= s= Use stat crunch to run a hypothesis test for mean. Go to stat → t-stats → one-sample →with summary Enter information about your sample. Enter your information for your null hypothesis and alternative hypothesis (make sure to select the appropriate inequality sign for your alternate hypothesis). Record your p-value: ____________ Based on your p-value, do you reject your null hypothesis or fail to reject your null hypothesis? Use a 0.01 significance level. Based on your answer to #4, does the sample data provide sufficient evidence that the mean BMI for 6-year-old girls has increased? Explain. 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

Answer 1

let us consider = mean BMI for current girls

(one tailed )

we have the following output from stat crunch

One-Sample T: BMI

Test of μ = 15.6 vs > 15.6

Variable N Mean StDev SE Mean 95% Lower Bound T P
BMI 30 16.173 2.669 0.487 15.345 1.18 0.125

x ̅=16.173

s= 2.669

p value is 0.125

since p value is greater than 0.01 so we are   fail to reject your null hypothesis

we do not have sufficient evidence to conclude that  the mean BMI for current girls is greater than 15.6