Question

Medical researchers conducted a national random sample of the body mass index (BMI) of 654 women aged 20 to 29 in the U.S. The distribution of BMI is known to be right skewed. In this sample the mean BMI is 26.8 with a standard deviation of 7.42. Are researchers able to conclude that the mean BMI in the U.S. is less than 27? Conduct a hypothesis test at the 5% level of significance using StatCrunch (directions) or calculating T and using the T-Distribution Calculator above. Based on your hypothesis test, what can we conclude?

Answer 1

Check the explanation

Explanation:

The distribution is right skewed but the sample size is large so we can use t - test here. The statistical software output for this problem is:

One sample T hypothesis test:

μ : Mean of population

`H_0` : μ = 27

`H_A` : μ < 27

Hypothesis test results:

Mean Sample Mean Std. Err. DF T-Stat P-value

μ 26.8 0.29014496 653 -0.68931061 0.2454

Since p - value > 0.05, do not reject .

Hence,

With a mean BMI of 26.8, the data supports the claim that the average BMI is less than 27, but the difference is not statistically significant. We fail to reject the null hypothesis that the mean BMI for women aged 20 to 29 in U.S. is 27.