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. Here is the t-test applet. Click here to open the applet.What can we conclude? 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. With a mean BMI of 26.8, the data supports the claim that the average BMI is less than 27. We reject the null hypothesis that the mean BMI for women aged 20 to 29 in U.S. is 27. Nothing. The distribution of the variable in the population is right skewed, so the conditions for use of a t-model are not met. We cannot trust that the p-value is accurate for this reason.

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Description: 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

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MATLAB: An Introduction with Applications

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Author:Amos Gilat

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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. Here is the t-test applet. Click here to open the applet.

What can we conclude?

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.
With a mean BMI of 26.8, the data supports the claim that the average BMI is less than 27. We reject the null hypothesis that the mean BMI for women aged 20 to 29 in U.S. is 27.
Nothing. The distribution of the variable in the population is right skewed, so the conditions for use of a t-model are not met. We cannot trust that the p-value is accurate for this reason.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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