Question

Do US adults consume an average of more than 75 grams of fat per day? According to a study of 600 adults in a scientifically designed study, the sample mean was 77.23 grams with sample standard deviation 33.47 grams. Do all the steps of a hypothesis test using normal theory methods, including finding the p-value, and write the conclusion in context.

Answer 1

Let X (be a random variable ) denotes the consumption of fat per day by US adults

We are given sample size n=600

Sample mean =77.23

Sample Standard deviation S = 33.47

We have to test whether the average mean is more than 75 g per day or not

For this, null and alternative hypotheses are:

Decision Rule:

If Calculated value of Z is greater than tabulated value of Z at , then we reject our null hypothess otherwise accept it.

Test Statistic :

Calculating its value, we get

Z = 1.631

The calculated value of Z is 1.631

At   , tabulated value of Z =1.96

Clearly Z calculated < Z tabulated, so we accept our null hypothesis i.e.