# Math 221 statistics for decision making Final Exam

Math 221 statistics for decision making

Final Exam

You should work each of the following on your own, then review the solutions guide. DO NOT look at the solutions guide first.

1. Explain the difference between a population and a sample. In which of these is it important to distinguish between the two in order to use the correct formula? mean; median; mode; range; quartiles; variance; standard deviation.

2. The following numbers represent the weights in pounds of six 7- year old children in Mrs. Jones’ 2nd grade class.

{25, 60, 51, 47, 49, 45}

Find the mean; median; mode; range; quartiles; variance; standard deviation.

3. If the variance is 846, what is the standard deviation?

4. If we have the following data

34, 38, 22, 21, 29, 37, 40, 41, 22, 20, 49, 47, 20, 31, 34, 66

Draw a stem and leaf. Discuss the shape of the distribution.

5. What type of relationship is shown by this scatter plot?

6. What values can r take in linear regression? Select 4 values in this interval and describe how they would be interpreted.

7. Does correlation imply causation?

8. What do we call the r value.

9. To predict the annual rice yield in pounds we use the equation

y ˆ = 859 + 5.76 x 1 + 3.82 x 2 , where x1 represents the number of acres planted (in thousands) and where x2 represents the number of acres harvested (in thousands) and where r 2 = .94.

a) Predict the annual yield when 3200 acres are planted and 3000 are harvested.

b) Interpret the results of this r 2 value.

c) What do we call the r 2 value?

10. The Student Services office did a survey of 500 students in which they asked if the student is part-time or full-time. Another question asked whether the student was a transfer student. The results follow.

Transfer Non-Transfer Row Totals

Part-Time 100 110 210

Full-Time 170 120 290

Column Totals 270 230 500

a) If a student is selected at random (from this group of 500 students), find the probability that the student is a transfer student. P (Transfer)

b) If a student is selected at random (from this group of 500 students), find the probability that the student is a part time student. P (Part Time)

c) If a student is selected at random (from this group of 500 students), find the probability that the student is a transfer student and a part time student. P(transfer ∩ part time).

d) If a student is selected at random (from this group of 500 students), find the probability that the student is a transfer student if we know he is a part time student. P(transfer | part time).

e) If a student is selected at random (from this group of 500 students), find the probability that the student is a part time given he is a transfer student. P(part time | transfer)

f) Are the events part time and transfer independent? Explain mathematically.

g) Are the events part time and transfer mutually exclusive. Explain mathematically.

11. A shipment of 40 television sets contains 3 defective units. How many ways can a vending company can buy five of these units and receive no defective units?

12. How do you recognize a discrete distribution?

13. The random variable X represents the annual salaries in dollars of a group of teachers. Find the expected value E(X).

X = {$35,000; $45,000; $55,000}.

P(35,000) = .4; P(45,000) = .3; P(55,000) = .3

14. How do you recognize a binomial experiment?

15. An advertising agency is hired to introduce a new product. The agency claims that after its campaign 61% of all consumers are familiar with the product. We ask 7 randomly selected customers whether or not they are familiar with the product.

a) Is this a binomial experiment? Explain how you know.

b) Use the correct formula to find the probability that, out of 7 customers, exactly 4 are familiar with the product. Show your calculations.

16. How do you recognize a Poisson experiment?

17. The mean number of cars per minute going through the Eisenhower turnpike automatic toll is about 7. Find the probability that exactly 3 will go through in a given minute using the correct table, formula, or Excel function.

18. How do you recognize a normal distribution?

19. Label the following as continuous or discrete distributions.

a) The lengths of fish in a certain lake.

b) The number of fish in a certain lake.

c) The diameter of 15 trees in a forest.

d) How many trees are on a farmer’s acre.

20. Jack weighs 160 pounds and his sister weighs 110 pounds. If the mean weight for men his age is 175 with a standard deviation of 14 pounds and the mean weight for women is 145 with a standard deviation of 10 pounds, determine whose weight is closer to “average.” Write your answer in terms of z-scores and areas under the normal curve.

21. On a dry surface, the braking distance (in meters) of a certain car is a normal distribution with mu = µ = 45.1 m and sigma = σ = 0.5

(a) Find the braking distance that corresponds to z = 1.8

(b) Find the braking distance that represents the 91st percentile.

(c) Find the z-score for a braking distance of 46.1 m

(d) Find the probability that the braking distance is less than or equal to 45 m

(e) Find the probability that the braking distance is greater than 46.8 m

(f) Find the probability that the braking distance is between 45 m and 46.8 m.

22. A drug manufacturer wants to estimate the mean heart rate for patients with a certain heart condition. Because the condition is rare, the manufacturer can only find 14 people with the condition currently untreated. From this small sample, the mean heart rate is 101 beats per minute with a standard deviation of 8.

(a) Find a 99% confidence interval for the true mean heart rate of all people with this untreated condition. Show your calculations.

(b) Interpret this confidence interval and write a sentence that explains it.

23. Determine the minimum required sample size if you want to be 80% confident that the sample mean is within 2 units of the population mean given sigma = 9.4. Assume the population is normally distributed.

24. A social service worker wants to estimate the true proportion of pregnant teenagers who miss at least one day of school per week on average. The social worker wants to be within 5% of the true proportion when using a 90% confidence interval. A previous study estimated the population proportion at 0.21.

(a) Using this previous study as an estimate for p, what sample size should be used?

(b) If the previous study was not available, what estimate for p should be used?

25. Suppose you are performing a hypothesis test on a claim about a population proportion. Using an alpha = .04 and n = 90, what two critical values determine the rejection region if the null hypothesis is

Ho: p = 0.54?

(a) ± 1.96

(b) =± 2.05

(c) ± 2.33

(d) none of these

26. A restaurant claims that its speed of service time is less than 15 minutes. A random selection of 49 service times was collected, and their mean was calculated to be 14.5 minutes. Their standard deviation is 2.7 minutes. Is there enough evidence to support the claim at alpha = .07. Perform an appropriate hypothesis test, showing each important step. (Note: 1st Step: Write Ho and Ha; 2nd Step: Determine Rejection Region; etc.)

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