STAT 201 Final, Spring 2002

Time: 2 hours June 13, 200 MATH 207 Final Exam Second Semester, 01-02 Instruction: Give answers correct to 2 decimal places. 1.For six weeks, a manager recorded the number of radio ads aired per week and the amount of sales (in thousands of dollars) of a certain product. The data for the sample follow. Number of ads x 2 5 8 8 10 12 Sales y $2 $4 $7 $6 $9 =©$10 a) Find the regression equation for the data. b) Use the equation found in (a) to predict the value of sales when x = 7 ads. 2. The mean time it takes adults to complete a certain achievement test is 46.2 minutes with a standard deviation of 8 minutes. Assume the variable is normally distributed. a) Find the probability that a randomly selected adult will complete the test in less than 43 minutes. b) Ifa randomly selected sampie of 49 adults take the test, find the probability that the mean time it takes the sample to complete the test will be less than 43 minutes. c) Compare the probabilities found in (a) and (b) and comment. 3. The amounts of telephone bills for all households in a large city have a distribution that is skewed to the right with a mean of $70 and a standard deviation of $25. LetX be the mean amount of telephone bills for a random sample of 90 households selected from this city. a) Calculate the mean and standard deviation of K and describe the shape of its probability distribution. b) What is the probability that the value of X lie within $2 of the population mean? 4.The standard deviation for a population is 6.3. Its unknown mean isp. A random sample of size n, selected from this population gave a mean equal to 78.9. a) Construct a 95% confidence interval for pb and give the width of the interval, in each of the following cases: (i) n=36 (ji) n=81 (iii) n=100 b) Does the width of the confidence intervals constructed in part (a) increase or decrease as the sample size increases? Why? eo) Heaney yey i ne . Ltr, RY OF BRP 5. Arandom sample of 25 families selected from an area showed that they spend an average of $120 per month on health care with a sample standard deviation of $28. Construct a 99% confidence interval for the mean health care expenditure per month incurred by all families in this area. Assume the monthly health care expenditures of ali families in this area have a normal distribution. 6. Ho:p=40, Ha: #40, n=64, X=384, O=6, 0.05 a) Perform the above hypothesis test. b) According to the result of the test in (a), what type of error might have occurred? Why? 7. The average SAT score in mathematics is 483,with a standard deviation of 100. A special preparation course claims that it can increase scores. A sample of 32 students completed the course and the mean of their scores was 503. a) At significance level of= 0.05, does the course do what it claims? Perform the appropriate hypothesis test. b) According to the result of the test in (a), what type of error might have occurred? Why?