Question 3.

The SPCA conducted a research into the recommended daily potassium in the diet for dogs and found that it should be 15 mg. A random sample of 45 dog food brands was conducted and the potassium in the food brands were analyzed and found that the sample mean was 13.3 mg. The population standard deviation is known to be 5.1 mg.

a. State the null and alternative hypotheses. Is this a 1-tail or 2-tail test?

b. Evaluate if there is evidence that the mean amount is different from 15 mg. Assume that the level of significance is 0.1.

c. Compute the p-value and interpret its meaning.

d. State Type I & II errors for this case. What is the probability of Type I error? How would you go about mitigating Type II errors?