# MATH 247

FINAL EXAM INFORMATION

Exam date and time:

Section 03        Friday, December 16                11:30 – 1:30

Section 04        Thursday, December 15           11:30 – 1:30

The final exam covers all chapters we’ve covered in class.

*You may omit the following sections / topics:

·        computing standard deviation of a sample by the formula

·        computing regression line using a formula

·        constructing a residual plot

·        Chapters 11 and 12 (except to the extent that the knowledge of population and sample is needed in the later chapters.)

Approximate credit distribution:           Chapters 1 – 6             20%

Chapters 7 – 9             15%

Chapters 14 – 16         20%

Chapter 18                   15%

Chapters 19 – 21, 23   30%

TI-83 calculators will be necessary on this exam.

You may bring one 8.5” by 11” page of notes.  The rules governing this sheet are:

1.                  You must make up your own sheet.

2.                  You must hand in the sheet with your exam.

3.                  The sheet may contain formulas, definitions and explanations.

4.                  The sheet may NOT contain specific examples.

I encourage you to make up your sheet early and study by trying problems using only the sheet.  I will provide the tables.

Office hours

Monday, 12/12              1:00 – 3:00 p.m.

Tuesday, 12/13              10:00 – 11:30 a.m., 2:30 – 3:30 p.m.

Wednesday, 12/14         10:30 – 11:45 a.m., 1:30 – 2:30 p.m.

Thursday, 12/15             9:30 – 11:00 a.m., 2:30 – 4:30 p.m.

### Other times are available by appointment

Final Exam Review problems

NOTE: It is NOT enough to only solve these problems to prepare for the final – they are just a sample (though not a random sample!) of some of the topics we’ve studied.

1.                 In a random sample of 125 children, 37 regularly have nightmares.  Use this data to find and interpret a 90% confidence interval for the proportion of all children who have nightmares.

2.                 The daily number of returns handled by one employee at a large mail order company was recorded for ten days.  These data are 28, 35, 32, 29, 48, 29, 30, 43, 36, 21.  Stating any assumptions you make, find and interpret a 95% confidence interval for the population mean number of returns.

3.                 A food service manager wants to be 95% certain that the margin of error in estimating of the mean number of sandwiches dispensed over the lunch hour is 10 or less.  What sample size should be selected if a preliminary sample suggests that s = 18?  What sample size would be required if s = 40?

4.                 With a random sample of size n = 144, someone has calculated a 95% confidence interval (using the Z-interval) of  (98, 106).

a.                    What was the mean of the sample?

b.                   What was the standard deviation of the population?

c.                    State what is wrong with this “interpretation” of the interval:  95% of the values in the sample are between 98 and 106.

5.             A researcher wants to know if there is a relationship between the heights of college women and the heights of the men they date.  She measures the heights of six pairs of dating couples.  The data is given here:

 Women 66 64 66 65 70 65 Men 72 68 70 68 71 75

a.                    Draw a scatter plot for this data.  Does there appear to be a correlation?  Describe what you see.

b.                   Find the equation of the linear regression line.  What does the line predict for the height of a man who is dating a woman who is 67 inches tall?

c.                    Find the sample correlation coefficient.  Interpret the coefficient.

6.             Past experience suggests that about 36% of all Christmas purchases are returned.  In a study of 247 purchases, 98 were returned.   Is there evidence to suggest that the percentage of returns has increased?  Use a level of significance of 0.05.  Also, find the p-value and explain its relevance.

1. Suppose the mileage on a randomly selected used car at a dealership is normally distributed with a mean of 28,766 miles, with a standard deviation of 2870 miles.
1. What percentage of cars have over 30,000 miles?
2. What percentage of cars have between 25,000 and 30,000 miles?
3. What is the 50th percentile for the mileage on a used car?  What is the 80th percentile?
4. If a sample of 20 cars is chosen at random, what is the probability that the mean mileage of that sample is greater than 30,000 miles?

1. Given the following data set:             12, 13, 10, 7, 15, 11, 11, 12, 18, 18, 23, 28, 20, 30, 13, 12
1. Construct a boxplot.
2. Construct a histogram with 5 or 6 classes.  Describe its shape.  How does it relate to the boxplot of the same data?

9.                    A bag contains 2 red balls, 3 blue balls and 1 yellow ball.  Suppose one ball is drawn out at random.

a.                    What is the probability of drawing a red ball?

b.                   Are the events “drawing a red ball” and “drawing a blue ball” disjoint?  Explain.

c.                    What is the probability that the ball is either blue or yellow?

d.                   Given that the ball is not blue, what’s the probability that it’s red?

e.                    How many red balls must be added to the bag so that the probability of drawing a red ball is ½?

10.                 What is false about each of the following statements?

1. Since there are 50 states, the probability of being born in Pennsylvania is 1/50.
2. The probability that I am taking math is 0.80 and the probability that I am taking English is 0.50, so the probability that I am taking math and/or English is 1.30.
3. The probability that the basketball team wins its next game is 1/3; the probability that it loses is ½.
4. The probability that Gary passes his biology course is 1.5.