Chapter 1 (Definitions)

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Jerome Newton
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1 FINAL EXAM REVIEW Chapter 1 (Definitions) Qualitative: Nominal: Ordinal: Quantitative: Ordinal: Interval: Ratio: Observational Study: Designed Experiment: Sampling: Cluster: Stratified: Systematic: Convenience: Simple Random:

2 Chapter 2 & 3 (Descriptive Statistics & Numerically Summarizing Data) 1. A city in the Pacific Northwest recorded its highest temperature at 96 degrees Fahrenheit and its lowest temperature at 28 degrees Fahrenheit for a particular year. Use this information to find the upper and lower limits of the first class if you wish to construct a frequency distribution with 10 classes. 2. Consider the data set: {31, 35, 30, 32, 29, 52, 38, 27, 28, 30} a. Create a stem and leaf plot. b. Determine IQR. c. What is the upper and lower fence for outliers? d. Are there any outliers? e. Create a box plot.

3 3. Determine the mean, median, mode, Q1, Q3, population standard deviation, sample standard deviation, population variation, sample variation of the following data set: 15, 11, 5, 8, 12, 6, 13, 11, 11, 8 Chapter 4 (Relationship of 2 Variables) 1. Find the linear regression line given the following data. x y

4 Chapter 5 & 6 (Probability & Discrete Probability Distributions) 1. What are the properties of a discrete probability distribution? 2. What is the missing probability if the only outcomes are 0, 1, 2, or 3? x P(x) If a card is randomly selected from a complete set of a standard deck of shuffle cards: A) P(red) = D) P(2) = B) P(face card)= E) P(15) = C) P(black jack)= 4. Use the data from the table of a random sample of 121 college students in Georgia to answer the following: Nonsmoker Smoker TOTAL Male Female TOTAL A) Find the probability of randomly selecting any person from the sample and the person being either a male smoker or a femalenonsmoker. B) Find the probability of randomly selecting a person from the group that is a smoker given that the person is a male? C) P(female smoker)

5 Chapter 7 (Normal Probability Distributions) 1. Find the area under the standard normal curve between z = 1.2 and z = Find P(z > 1.8) 3. The average overall score on the SAT last year was a 1500 with a standard deviation of 300. The average overall score on the ACT last year was 21 with a standard deviation of 5. a. What is the z score associated with a student scoring a 1750 on the SAT? b. What is the z score associated with a student scoring a 25 on the ACT? c. Which score is better? Chapter 8 (Sampling Distributions) 1. (Central Limit Theorem) The mean height of a male in the United States is roughly 69 inches (5 feet 9 inches) with a standard deviation of approximately 3 inches. a. Given samples of size 16 were randomly taken, what would be the mean of the sample means ( ) and the standard deviation of the sample means ( )? b. A random sample of 16 males from the United States was taken. What is the probability that the average height of the group was greater than 6 feet (72 inches)?

6 Chapter 9 (Confidence Intervals) 1. The population standard deviation of the SAT is known to be 300 and the population is approximately normal. If a random sample of 16 students had a mean score of 1560, construct a 99% confidence interval for the population mean. 2. A random sample of 16 females from the United States was taken. The mean height of the females from the sample was 64 inches and the sample standard deviation was 4 inches. Construct a 95% confidence interval for the population mean. 3. Given a sample {13, 15, 19, 10, 13, 12, 10, 18, 12, 12} construct a 90% confidence interval for the population mean.

7 Chapter 10 (Hypothesis Testing) 1. An environmental agency wants to see if the new government policies have helped the auto industry to increase fuel efficiency of compact car models. Five years ago the average fuel efficiency was 22 mpg. a. State the null hypothesis. b. State the alternate hypothesis. c. What would a Type I error suggest? d. What would a Type II error suggest? 2. If we wish to support the claim 20 at a level of signiicance of = Given the sample statistics n = 30, =19.2 and =4, a. What is the null hypothesis (H0)? b. Compute the value of the test statistic. c. What are the critical t values? d. What does the test statistic suggest?

8 3. A consumer group believes that a particular company that makes snacks is giving less than the amount of chips that is labeled on the bag. The bag suggests the weight of chips to be 24 grams. The group takes a random sample of 30 bags and finds the sample mean to be 23 grams with a standard deviation of 0.8 grams. a. State H0 and H1 b. Compute the test statistic. c. Determine the critical t value. d. Should we reject or fail to reject H0? (using = 0.01) 4. If we wish to support the claim 20 at a level of significance of = Given the sample statistics n = 16, =22, =4, and that the population is approximately normal, determine the P value. 5. If we wish to support the claim 20 at a level of significance of = Given the sample statistics n = 25, =18, s = 2, and it has been concluded that the sample appears to come from a population that is normally distributed based on a normality probability plot. a. Find the standardized test statistic t. b. Find the P Value using a t distribution.

9 Chapter 11 and 12 (Inference about 2 means & Chi Squared) 1. Using an inference about two means of independent samples. Attempt to validate the claim 1 2 at a level of significance of = The provided statistics: n1 = 16, 1=18, s1 = 2 and n2 = 16, 2=22, s2 = 3 a. Find the standardized test statistic t. b. Find the P Value using a t distribution. 2. Using = 0.10 and a Chi Square test of goodness of fit determine the following. Cards are drawn one at a time with replacement from a standard deck of shuffled cards and the frequency that each suit appears is recorded. Each suit should appear approximately ¼ of the time when selected. A player suspects that the deck is not standard because too many clubs are appearing. The results of the 100 random draws are shown below. Suit Hearts Clubs Diamonds Spades Frequency A) State H0. B) State H1. C) Find the chi square test statistic. D) Find the p value. E) What is the conclusion?

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Final Exam Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A researcher for an airline interviews all of the passengers on five randomly