Math 112 Elementary Statistics Fall 2006

Name (Print)______

Math 112 Elementary Statistics Fall 2006 Final Exam 150 Points Total Good Luck! Directions:  Whenever possible draw and shade corresponding area!  Must show logical work for full credit!  Box answers when possible!

I. Define the following terms: (2 points each, roman numeral I - IV)

1. Sample:

______

2. Population:

______

3. Standard Deviation: ______

______

4. Parameter: ______

______

5. Random Sample: ______

______

6. Statistic (This is not the word statistics!)______

of 6 Name (Print)______

II. Give an example of the following types of data:

a. Discrete Data:

b. Continuous Data:

c. What kind of data is “a” or “b” Quantitative or Qualitative

d. Give an example of Qualitative data:

III. True or False

a. The probability of an impossible event is 0. T or F

b. The probability of an event that is certain is 1. T or F

c. Probability can be negative on rare occasions. T or F

d. Two events are independent if the occurrence of one does not affect the probability of the occurrence of the other. T or F

e. For a data set that has a distribution that is approximately bell shape about 95% of all values lie with 2 standard deviation from the mean. T or F

f. Student t-distribution is used to test claim about the mean when sigma is known. T or F

g. Chi square is used to test claim about standard deviation or variance T or F

h. F-distribution is used to compare variances between two samples. T or F

i. The normal distribution is a continuous distribution. T or F

j. Standard normal distribution has a mean 0 and standard deviation 1. T or F

IV. Name the unbiased estimators that target the population parameter. 1. ______

2. ______

3. ______

V. Construct a relative frequency table and histogram for the given frequency distribution. Draw the graph neatly; label the horizontal axis and vertical axis. (12 points)

Incomes Frequency 200.300 69 301.400 73 401.500 81 501.600 65 >600 16

VI. For a large data set of average student grades, the third quartile Q3 is found to be 78.5. What does this mean when we say that 78.5 is the third quartile? (6 points)

VII. What is the difference between a standard normal distribution and a nonstandard normal distribution? (6 points)

VIII. Assume that X has a normal distribution, find the indicated probability. (12 points) “mu” is 137, “sigma” = 5.3 Find the probability that X is between 134.4 and 140.1

IX. Assume man’s highs are normally distributed with = 63.6 in and  = 2.5 in. (14 points) a. If a man is randomly selected find the probability that his height is between 63.5in and 64.5 in.  

b. If 16 man are normally selected, find the probability that they have a mean height between 63.5 in and 64.5 in.

X. In a sample of 70 students, 42 plan to graduate next year. Find the 95% confidence interval for the percentage of students planning to graduate next year. (12 points)

XI. The weights of 19 boxes of cereal are measured. The sample standard deviation is 0.18 ounces. The sample mean is 14.91 oz. We are concerned that the mean weight of all boxes may be under 15 oz. ( 14 points)

a. State the null and alternative hypothesis. b. Test the null hypothesis at the 5% level, using either p-value or classical approach, showing calculation of the test statistic. Word final conclusion in terms of original claim.

XII. Each person in a group of 300 students was identified as male or female and then asked whether he or she preferred taking liberal arts courses in the area or math-science, social science, or humanities. The table below shows the frequency found in these categories. Does the sample present sufficient evidence to reject the null hypothesis: “Preference for math-science, social science, or humanities is independent of the gender of a college student? Complete the hypothesis test using the 0.05 level of significance. (12 points)

Gender Math-Science Social Science Humanities Total Male 37 41 44 Female 35 72 71 Total

XIII. Twenty-five newspapers readers were asked how much time, estimated to the nearest minute they spend reading yesterday’s newspaper. Their times are listed by the age category of the reader. (15 points)

-Age- X= time 18-24 25-29 30-34 35-49 50-64 65 and up spent 10 13 14 20 20 8 reading 5 8 7 12 12 30 newspaper 15 20 20 5 18 35 yesterday 4 10 28 15 20 15 30

Use the one way ANOVA technique to test the claim that a person’s age has an effect on the average amount of time spent daily reading the newspaper? Use alpha 0.05. a. Set up the null and alternative hypothesis. b. Display calculator results in the ANOVA table below

Source Sum or Degrees of Mean F P-value Squares Freedom Square (SS) (df) Error (MS) Treatment Error Total

c. Test the hypothesis and word final conclusion in terms of original claim.