Silver Gym Analysis

PART I

Calculate the mean, median, range, and standard deviation for the Body Fat vs. Weight Data Set.

Body Fat Weight

Mean 18.94 178.92

Median 19.0 176.00

Range 45.1 244.65

Standard Deviation 7.75 29.33

Interpretations:

Mean is the numbers all added together and then divided by the number of the sample.

Median is the data set that is the middle number when the set is related in a numerical order.

Standard Deviation is the measure of the variable.

The mean in this case is that the bodyfat of the average man falls between 3.4% and 34% and the body weight falls between 120.1 and 230.7 pounds.

Range is the difference between the minimum and maximum numbers.

The mean and median are important because they are two ways of showing the typical value.

The mean can be more important when we want to represent all the variability, and there are no significant outliers. The median is a better measure when the data is skewed or there are a lot of outliers.

The range and standard deviation are important factors because they show the variability of the product.

Ranges can show the probability of the factor. Whereas Standard Deviation shows the inferences about the data. It shows how likely the values will fall within a standard range.

PART II

a. H0: mu = 20

mu < > 20

b.

I used A test for means. That's because the sample size is large, and we're comparing one sample to a specific number.

Critical value of Z two-tailed at alpha = 0.05 is +/- 1.96

Z = (xbar - µ)/(σ/√n)

Z = (18.9 - 20 )/(7.8/√252)

Z = -1.1 / (7.8/15.8745)

Z = -2.2387

Since Z < -1.96, there is enough evidence to determine that the hypothesis is a null hypothesis. The mean is not 20%

I'd tell my boss that the hypothesis test showed that the mean was significantly different from 20%, and that it's actually lower than the 20%.

Part