Question

1. Let X be a random variable that represents the weights in kilograms (kg) of a healthy adult female deer (doe) from Mesa Verde National Park. X has a distribution that is approximately normal with µ = 63.0 kg and standard deviation σ = 7.1 kg. A doe is considered to be malnourished if it weighs less than 54 kg.

a. If the doe population is healthy, what is the probability that a single doe captured weighs less than 54 kg?

b. What is the probability that the mean weight of a random sample of 50 does is less than 54 kg?

c. Create a 95% confidence interval for the mean weight of a random sample of 36 does in Mesa Verde National Park.

2. A CPA firm is auditing the accounts of a large interstate banking system. Out of a random sample of 152 accounts, it was found that 19 had transaction errors. Let p be the number of accounts with transaction errors.

a. Find a point estimate for p ( pˆ ):

b. Find a 99% confidence interval for p: . An article in the local paper claims that the average amount spent in a visit to a fast food restaurant is $20. Is the fast food restaurant in problem #1 unusually inexpensive? (In other words, are people spending less at the local fast food restaurant than the population does at an average fast food restaurant?) Assuming that the amount people spend is normally distributed, conduct a hypothesis test using a 5% significance level. a. Ho: Ha: b. Is this a right-tailed, two-tailed or left-tailed test?

c. Compute the z or t test statistic. Show the correct computation.

d. Find the p-value for the test statistic. e. Based on your answers above, do you reject or fail to reject the null hypothesis? What do you conclude about the average cost of this fast food restaurant?

Answer 1