Question

1.) Egg Beaters are egg substitutes with no fat or cholesterol. They are suppose to have 5 grams of protein in them. A quality control worker for Egg Beaters wants to assess if the mean amount of protein is different than 5 grams. They take a random sample of 18 Egg Beaters and obtain a sample mean of 5.07 grams of protein and a standard deviation of 0.94 grams of protein. Conduct a hypothesis test at the 5% significance level that corresponds with the quality control worker's investigation. Make sure to give the hypotheses, test statistic, p-value, decision, and a practical interpretation.

2.) It is known that the mean amount of iodine in cow's milk is 88 micrograms/250 ml. A researcher believes it is lower in milk from organic farms. A random sample of 35 one-gallon containers of milk was obtained from organic farms. The sample mean is 86.5 micrograms/250 ml and the standard deviation is 3.4 micrograms/250ml. Test the researcher's belief at the 10% significance level. Make sure to give the hypotheses, test statistic, p-value, decision, and a practical interpretation.

Answer 1

1)

Below are the null and alternative Hypothesis,
Null Hypothesis: H0 : μ = 5
Alternative Hypothesis:Ha : μ ≠ 5

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (5.07 - 5)/(0.94/sqrt(18))
t = 0.316

P-value Approach
P-value = 0.7558
As P-value >= 0.05, fail to reject null hypothesis.

There is not sufficient evidence to support the claim that the mean amount of protein is different than 5 grams

2)

Below are the null and alternative Hypothesis,
Null Hypothesis: H0 : μ = 88
Alternative Hypothesis:HA : μ < 88

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (86.5 - 88)/(3.4/sqrt(35))
t = -2.61

P-value Approach
P-value = 0.0067

As P-value < 0.1, reject the null hypothesis.

There is sufficient evidence to support the claim that it is lower in milk from organic farms