Question

1. A food manufacturer claims that their new oat bran muffin has a population mean calorie content of 250 calories with a sample standard deviation of 10.1 calories. A government food researcher believes the manufacturer's claim is too low and decides to test the manufacturer's claim. A random sample of 25 muffins yields a sample mean calorie content of 254.9 calories. The food researcher decides to perform a hypothesis test at

α = 1 % to determine if it is reasonable to reject the manufacturer’s claim.

1. State the hypotheses (in words & symbols):

H0:

Ha:

0. 2. Determine the model to test H0
1. Can you use a normal distribution for the Sampling Distribution model to perform this test? Please explain. If not, then what distribution could you use?

2. Using the appropriate notation, state the MEAN & STD ERROR of the sampling distribution: Mean:

STD Error:

3. Determine the Decision Rule:

State the decision rule:

4. Analyze the sample data: Using the appropriate notation, state the sample result used to perform the test, p-value and the test statistic. Draw the Hypothesis Testing Model with the decision rule and test statistic on the diagram.

sample result (use appropriate notation) is:

p-value ( to 4 decimal places ) is:

test statistic (use appropriate notation) is:

Hypothesis Testing Model:

5. State the Conclusion:

Answer 1

Since observed value of test statistic falls in rejection region, we reject H0 at 1% level of significance at 1% level of significance.

There is sufficient evidence to accept the believe of the government food researcher that the manufacturer's claim is too low.