i) State the Hypotheses to Test.

ii) Make a decision based on the information given.

iii) What would be Type I or Type II error.

• An investigator hypothesizes that cholesterol levels in children might be affected by educating their parents on proper nutrition and exercise. A sample of 40 families with a child between the ages of 10-15 who has been diagnosed with high cholesterol agree to participate in the study. All parents are provided educational information on nutrition and exercise. After following the prescribed program, their child's total cholesterol level is measured. The children's mean cholesterol level is 175 with a standard deviation of 19.5. Is there significant evidence of a reduction in total cholesterol in the children? The Z test p-value is 0.0674. The initial children's mean total cholesterol level was 180.

• Recent recommendations suggest 60 minutes of physical activity per day. A sample of 150 adults in a study of cardiovascular risk factors report exercising a mean of 38 minutes per day with a standard deviation of 19 minutes. Based on the sample data, the researcher wants to test if the average time of physical activity is significantly less than the recommended at a 5% level of significance and observed a 95% CI of (23, 53).
• A study is conducted to compare mean cholesterol levels for individuals following a low carbohydrate diet for at least 6 months to individuals following a conventional (low-fat, low calorie) diet for at least 6 months. The data are summarized below:

Diet Program	Sample Size	Mean Cholesterol	Std Dev Cholesterol
Low Carbohydrate	50	225.4	24.5
Conventional	75	203.8	21.6

Test if there is a significant difference in mean cholesterol levels between the diet programs using a 5% level of significance. The Z test p-value is less than 0.0001.

• The mean lifetime for cardiac stents is 8.9 years. A medical device company has implemented some improvements in the manufacturing process and hypothesizes that the lifetime is now longer. A study of 40 new devices reveals a mean lifetime of 9.7 years with a standard deviation of 3.4 years. Is there statistical evidence of a prolonged lifetime of the stents? The Z test p-value is 0.0691.

• A study is performed to examine the relationship between the concentration of plasma antioxidant vitamins and cancer risk. The table below shows data for plasma vitamin-A concentration in stomach-cancer patients and in controls (participants similar to the cancer patients but free of disease). Is there a significant difference in the mean concentration of plasma antioxidant vitamins between patients with stomach cancer and controls? The Z test p-value is less than 0.01.

	N	Mean	Std Dev
Stomach cancer patients	20	2.41	0.15
Controls	50	2.78	0.19