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MATH 342 STATISTICS EXAM 1 Due 2/17/2009

_1. (12) Let’s say you’ve been assigned to study the efficiency of bank tellers at Fourth Second Bank (FSB). FSB has twenty-one branches in three states. Your measure of efficiency is the time (in seconds) it takes to complete a transaction. Address the following points for this study.

a. (2) What is the population? (Use the more technical definition I gave in class.)

b. (2) What parameter should be estimated?

c. (4) Describe how internal validity can be maximized.

d. (4) Describe how external validity can be addressed.

_2. (4) Why is median used as a measure of central tendency, when the arithmetic mean is so easy to compute? Describe a situation where the median would be a preferable to the mean.

_3. (4) If n = 1097, what is the position of the median? What needs to be done first to the sample in order to calculate the median?

_4. (10) Classify each of these variables as either (1) quantitative or (2) qualitative.

_____ Favorite colors of automobiles

_____ Type of graffiti on classroom desks (light-hearted, hateful, obscene)

_____ Classification of children in day care (infant, toddler, preschool)

_____ Number of pages in statistics textbooks

_____ Hours per week that LPNs work in a particular hospital

_5. (7) The SAT math section has population mean and standard deviation 460 and 100 respectively. The corresponding parameters for the ACT math section are 21 and 4. Which score would be “better” – 660 on the SAT or 30 on the ACT? Why? Show your work!

_6. (6) Describe the population in each of the following popular summaries of studies. Use the definition of population I gave in class.

a. “The average amount spent per gift for Mom on Mother’s Day is $26.85.”

b. “More than 1 in 4 American children have cholesterol levels of 180 mg or higher.”

_7. (12) Calculate the mean, median, and standard deviation for the following sample of teller transaction times. Show your work! {1, 4, 6, 3, 10, 5, 6, 2}

_8. (16) For each of these three problems, draw a sketch and do all the steps we did in class. Light bulbs manufactured by the Acme Corporation last on the average 300 days with a standard deviation of 50 days. Assuming that population of bulb lives is normally distributed, what is the probability that an Acme light bulb will last

a) at most 365 days?

b) between 240 and 350 days?

c) If a sample of size n = 81 is taken from this population what is the probability that its mean is 290 and 310 days?

d) Again for samples of size n = 81, what interval (between what two values?) contains the middle 95% of means of samples of size n = 81? (In other words, if you plan to take a valid random sample of bulb lives of size n = 81, between what two values would there be a 95% probability that your actual sample mean would lie?)

_9. (8) In a normal distribution, what z-score corresponds to each of these percentiles?

a) 25^th b) 40^th c) 80^th d) 95^th

_10. (5) Molly earned a score of 940 on a national achievement test whose scores are normally distributed with μ = 850 and σ = 100. What proportion of students had a higher score than Molly? Show work to justify your answer.

a) 0.10 b) 0.18 c) 0.50 d) 0.82 e) 0.90

_11. (16) A brisk walk at 4 miles per hour burns an average of µ = 300 Calories per hour with σ = 8 Calories per hour. Supposing that this distribution is normal, calculate the probability that a randomly-selected person who walks 1 hour at a rate of 4 miles per hour will burn

a) more than 302 Calories. b) between 297 and 302 Calories.

If n = 64 people are involved in a valid random sample of Calories per hour burned by taking brisk walks at 4 miles per hour, calculate the probability that the mean of this sample is

c) more than 302 Calories. d) between 297 and 302 Calories.