105年 - 105 國立交通大學管碩士班考試入學試題：統計學#123985

(1) Develop a 95% confidence interval for the population mean daily spending. (5 points)

(2) Interpret the confidence level in the previous question. (5 points)

(3) What level of confidence is associated with an interval of $58.62 to $68.52 for the population mean daily spending? (5 points)

(1) Calculate E(XY). (2 points)

(2) Are X and Y independent? Explain. (2 points)

(3) Calculate Cov(X,Y). Did you expect this answer? Why? (2 points)

(4) Find the probability distribution of the random variable X+ Y. (2 points)

(5) Show that Var(X+Y) = Var(X) + Var(Y). Did you expect this result? Why? (2 points)

(1) What is the probability that a spinning machine just placed back in service will need maintenance before it produces 4 miles of wire? (5 points)

(2) What is the median amount of time before the machine needs servicing? (5 points)

(3) You are the Webmaster for your firm's Website. From your records, you know that the probability that a visitor will buy something from your firm is 0.23. If the number of visitors in one day is 952, what is the probability that less than 200 of them will buy something from your firm? Use the normal approximation for the binomial. (5 points)

(1) Find the population mean and population standard deviation. (5 points)

(2) List all possible samples of 2 households that can be selected without replacement from this population, and compute the sample mean for each sample. (5 points)

(3) Use your answer to the previous question to determine the sampling distribution of sample means. (5 points)

(1) Carefully explain what is meant by the p-value of a test, and discuss the use of this concept in hypothesis testing. (5 points)

(2) Does this provide strong evidence that the people in Great Britain are more optimistic about the economy? (10 points)

(1) Interpret the linear regression of recovery time on dosage level (Y=73.65-36.98X),and find the t-value of the slope estimated (Hint: the standard error of the slope is 12.2173). (10 points)

(2) Find and interpret a 90% confidence interval for the slope of the population regression line. Discuss how the critical values of the confidence interval are determined. (15 points)

(3) Would the sample regression derived in part (1) be useful in predicting recovery time for a patient given 2.5 grams of this drug? Explain your answer. (5 points)