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Use the given sample data (midterm_data.dta) to answer this question.

INSTRUCTIONS TO CANDIDATES
ANSWER ALL QUESTIONS

1. Use the given sample data (midterm_data.dta) to answer this question.

a. What is the sample mean and standard deviation of the number of steps walked daily?   (2 points)

b. Calculate and interpret the 90% confidence interval for the average number of steps walked daily.   (4 points)*

c. Assume that another random sample of 20 people gave you the same mean and standard deviation as obtained in part (a). Calculate and interpret the new 90% confidence interval for the average number of steps walked daily. Explain in 1-2 sentences why this new 90% C.I. is wider or narrower than the one calculated in part (b).   (4 points)*

2. The annual amount (i.e., weight) of food wasted by households is normally distributed, with a mean of 228 pounds and a standard deviation of 52 pounds.

a. What is the probability of a household wasting more than 200 pounds of food in a year?   (3 points)*

b. What is the probability of a household wasting between 250 and 300 pounds of food in a year?   (3 points)*

c. How much food (in pounds) will the best 10% households (i.e., those that waste the least amount of food) waste in a year?   (4 points)*

3. Based on the given sample data (midterm_data.dta), can we conclude that the proportion of people in the population who are from Colorado is significantly different from 30%?

a. What is the sample proportion of people who are from Colorado?   (2 points)*

b. State the null and alternate hypotheses.   (2 points)

c. What is the decision rule?   (2 points)

d. What is the value of the test statistic?   (1 point)

e. What is the decision? Interpret this decision in 1 sentence.   (2 points)

f. What is the p-value?   (1 point)

4. There is a 14% chance that an adult in Denver will wear a mask in public when not mandated. An adult in Denver will either wear a mask or they will not. The probability of an adult in Denver wearing a mask is independent of the probability of any other adult in Denver wearing a mask. There are 10 adults present in a particular store in Denver.

a. What is the probability that at least one adult in this store is wearing a mask?   (4 points)*

 

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