Math 116 Study Guide for Final Exam

$Math 116 Study Guide for Final Exam$

Math 116 – Study Guide for final exam

1. Terminology

Statistics vs. parameter

Quantitative variable (discrete, continuous) vs Qualitative variable

Population vs Sample

Sampling techniques

Simple random sample

Stratified sampling

Systematic sampling

Convenience sampling

Observational study vs Experiment

Placebo effect

Completely randomized experiment

Control group vs Treatment group

Double blind experiment

Lurking or confounding variable

Regression: R vs R2

2. Measures of central tendency

Average

Mean

Notations for samples and for populations

Median

Mode

3. Measures of variation

Range

Standard deviation

Notations for samples and for populations

Variance

Interquartile range, IQR

Five-number summary

Outliers

Box and whisker plots

4. The Standard Normal Distribution

Use the formula to find the z-score corresponding to a given score
Use the formula to find scores corresponding to a given z-score
Know what the parameters of the standard normal distribution are
Know the relationship between probabilities/percentages/areas under the normal curve (or any distribution)
Use the standard normal table (table 5) to find

a) Areas to the left of a given z score

b) Areas to the right of a given z score

c) Areas between any two given z scores

For any normally distributed variable, find areas under the normal curve

To the right, left or between any two values of the variable

5. Sampling Distributions for Means

Understand what the distribution of sample means is
Understand The Central Limit Theorem
Identify the shape, mean and standard deviation of the distribution of sample means for a given sample size n, for a normally distributed variable

6. Estimating Population Parameters (, or p)

Understand the objective of constructing confidence intervals
Know the vocabulary: confidence level, point estimate, margin of error, standard error, critical value, lower and upper limits
Be familiar with the assumptions related to each of the procedures
Find the margin of error, and interpret its meaning
Construct a confidence interval for the population mean using the formulas

a) When σ (the standard deviation of the population) is given

b) When σ is NOT given (you only have access to s, the standard deviation of the sample

Construct a confidence interval for the population proportion using the formulas
Interpret the results within the context of the problem
Find the sample size in order to estimate the mean of a population with a certain degree of confidence and a given margin of error
Hypothesis testing
Null and alternative hypothesis
Calculate test statistic
Compute p value from table/and or calculator
Decide whether to accept or reject null hypothesis

6. Two Sample Study

Construct a confidence interval for the population mean

Hypothesis testing

Null and alternative hypothesis
Calculate test statistic
Compute p value from table/and or calculator
Decide whether to reject or fail to reject the null hypothesis/ but mainly whether you support / or do not have enough evidence to support the alternative hypothesis which will be the claim (most of the time)

7. Chi Square

Count vs, expected frequency
Hypothesis testing
Null and alternative hypothesis
Calculate chi=square test statistic
Compute p value from table/and or calculator
Decide whether to accept or reject null hypothesis

Practice problems, final exam

1.Given the sample data below, use the defining formula to compute the sample standard deviation.

13 32 28 13 12 23

a)8.71

b)24.20

c)63.14

d)75.77

e)7.95

2.Find the range for the following sample data.

/ 23 / 19 / 15 / 31 / 26

a)7

b)8

c)4

d)5

e)16

3.If event A is certain to occur, what is P(A)?

a)0

b)0.25

c)0.5

d)0.75

e)1

4.A coin is to be tossed 1000 times. What is the probability that the 785th toss is heads?

a)0

b)1/4

c)1/2

d)3/4

e)1

5.Identify the variable in the information below.

USA Today reported that 44.9% of those surveyed (1261 adults) ate in a fast-food restaurant from one to three times each week.

a)fast-food restaurant as well as response regarding frequency of eating at fast-food restaurants

b)adults surveyed

c)fast-food restaurants

d)response regarding frequency of eating at fast-food restaurants

e)none of these choices

6.Identify whether the variable in the information below is qualitative or quantitative.

Government agencies carefully monitor water quality and its effect on wetlands (Reference: Environment Protection Agency Wetland Report EPA 832-R-93-005). Of particular concern is the concentration of nitrogen in water draining from fertilized lands. Too much nitrogen can kill fish and wildlife. Twenty-eight samples of water were taken at random from a lake. The nitrogen concentration (milligrams of nitrogen per liter of water) was determined for each sample.

a)quantitative

b)qualitative

c)qualitative as well as quantitative

d)neither qualitative nor quantitative

e)Information does not have any variable.

7.Find the technique for gathering data in the study below.

The Colorado Division of Wildlife imposed special fishing regulations on the Deckers section of the South Platte River. All trout under 15 inches had to be released. A study of trout before and after the regulations went into effect showed that the average length of trout increased by 4.2 inches after the new regulations.

a)observational study

b)experiment

c)census

d)sampling

e)none of these choices

8.Give an example of a discrete random variable.

a)The number of inches of rainfall in a county

b)The number of beverages sold at a lemonade stand

c)The number of gallons of concrete used at a construction site

d)The time required for a runner to finish a marathon

e)The temperature of a pot roast cooking in an oven

9.Assuming that the heights of college women are normally distributed with mean 65 inches and standard deviation 2.5 inches, what percentage of women are taller than 67.5 inches?

a)0.1%

b)15.9%

c)97.7%

d)50.0%

e)84.1%

10.Assuming that the heights of college women are normally distributed with mean 68 inches and standard deviation 2.5 inches, what percentage of women are shorter than 63 inches?

a)2.3%

b)97.7%

c)84.1%

d)0.1%

e)50.0%

11.Assuming that the heights of college women are normally distributed with mean 63 inches and standard deviation 2 inches, what percentage of women are between 63 inches and 67 inches?

a)13.6%

b)47.7%

c)34.1%

d)97.6%

e)15.7%

12.Suppose a certain species of fawns between 1 and 5 months old have a body weight that is approximately normally distributed with mean kilograms and standard deviation kilograms. Let x be the weight of a fawn in kilograms. Convert the following x interval to a z interval. Round to the nearest hundredth.

13.Find the area under the standard normal curve over the interval specified below.

Between and

a)0.341

b)0.499

c)0.136

d)0.477

e)0.819

14.Find the area under the standard normal curve over the interval specified below.

To the right of

a)0.841

b)0.159

c)0.999

d)0.500

e)0.977

15.A person's level of blood glucose and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean and standard deviation of What is the probability that, for an adult after a 12-hour fast, x is more than 119?

a)0.486

b)0.971

c)0.236

d)0.471

e)0.029

16.Give an example of a population.

a)Seven cards chosen at random from a 52-card deck

b)A week of television shows watched by Americans as reported in a survey

c)The lengths of all trout in a lake

d)The automobiles bought by Americans polled in a telephone survey

e)Registered Oklahoma voters who voted in a U.S. presidential election

17.What is a parameter?

a)A conclusion about the value of a population parameter based on information about the corresponding sample statistic and probability

b)A numerical descriptive measure of a population

c)A set of measurements (or counts), either existing or conceptual

d)A probability distribution for a sample statistic

e)A numerical descriptive measure of a sample

18.Which of the following variables does NOT signify a parameter?

b)µ

e)p

19.What is a statistic?

a)A conclusion about the value of a population parameter based on information about the corresponding sample statistic and probability

b)A numerical descriptive measure of a population

c)A set of measurements (or counts), either existing or conceptual

d)A probability distribution for a sample statistic

e)A numerical descriptive measure of a sample

20.Which of the following variables does NOT signify a statistic?

a)s

c)µ

21.What is a sampling distribution?

a)A conclusion about the value of a population parameter based on information about the corresponding sample statistic and probability

b)A numerical descriptive measure of a population

c)A set of measurements (or counts), either existing or conceptual

d)A probability distribution for a sample statistic

e)A numerical descriptive measure of a sample

22.Suppose that x has a distribution with = 18 and = 6. If a random sample is taken of size n = 40, find .

a)18.00

b)0.95

c)2.85

d)0.15

e)6.00

23.Suppose a certain species bird has an average weight of grams. Based on previous studies, we can assume that the weights of these birds have a normal distribution with grams. For a small group of 18 birds, find a 70% confidence interval for the average weights of these birds.

a)2.81 grams to 4.17 grams

b)2.81 grams to 3.93 grams

c)3.77 grams to 4.17 grams

d)3.77 grams to 3.93 grams

e)3.53 grams to 3.92 grams

24.A random sample of 318 medical doctors showed that 127 had a solo practice. As a news writer, how would you report the survey results regarding the percentage of medical doctors in solo practice? What is the margin of error based on a 95% confidence interval?

a)A recent study shows that about 60% of medical doctors have a solo practice with a margin of error of 2.7 percentage points.

b)A recent study shows that about 60% of medical doctors have a solo practice with a margin of error of 5.4 percentage points.

c)A recent study shows that about 40% of medical doctors have a solo practice with a margin of error of 2.7 percentage points.

d)A recent study shows that about 40% of medical doctors have a solo practice with a margin of error of 10.8 percentage points.

e)A recent study shows that about 40% of medical doctors have a solo practice with a margin of error of 5.4 percentage points.

25.A severe storm has an average peak wave height of 16.4 feet for waves hitting the shore. Suppose that a storm is in progress with a severe storm class rating. Let us say that we want to set up a statistical test to see if the wave action (i.e., height) is dying down or getting worse. If you wanted to test the hypothesis that the waves are dying down, what would you use for the alternate hypothesis? Is the P-value area on the left, right, or on both sides of the mean?

a) is greater than 16.4 feet; the P-value area is on both sides of the mean

b) is greater than 16.4 feet; the P-value area is on the left of the mean

c) is not equal to 16.4 feet; the P-value area is on the right of the mean

d) is not equal to 16.4 feet; the P-value area is on the left of the mean

e) is less than 16.4 feet; the P-value area is on the left of the mean

26.Suppose that the mean time for a certain car to go from 0 to 60 miles per hour was 6.7 seconds. Suppose that you want to set up a statistical test to challenge the claim of 6.7 seconds. What would you use for the null hypothesis?

a) seconds

b) seconds

c) seconds

d) seconds

e) seconds

27.A professional employee in a large corporation receives an average of e-mails per day. Most of these e-mails are from other employees in the company. Because of the large number of e-mails, employees find themselves distracted and are unable to concentrate when they return to their tasks. In an effort to reduce distraction caused by such interruptions, one company established a priority list that all employees were to use before sending an e-mail. One month after the new priority list was put into place, a random sample of 49 employees showed that they were receiving an average of e-mails per day. The computer server through which the e-mails are routed showed that Has the new policy had any effect? Use a 5% level of significance to test the claim that there has been a change (either way) in the average number of e-mails received per day per employee. What are the null and alternate hypotheses?

a) e-mails; e-mails

b) e-mails; e-mails

c) e-mails; e-mails

d) e-mails; e-mails

e) e-mails; e-mails

28.Let x be a random variable representing dividend yield of Australian bank stocks. We may assume that x has a normal distribution with A random sample of 24 Australian bank stocks has a mean For the entire Australian stock market, the mean dividend yield is Do these data indicate that the dividend yield of all Australian bank stocks is higher than 5%? Use What is the level of significance?

a)0.900

b)0.050

c)0.950

d)0.975

e)0.100

29.A professional employee in a large corporation receives an average of e-mails per day. Most of these e-mails are from other employees in the company. Because of the large number of e-mails, employees find themselves distracted and are unable to concentrate when they return to their tasks. In an effort to reduce distraction caused by such interruptions, one company established a priority list that all employees were to use before sending an e-mail. One month after the new priority list was put into place, a random sample of 46 employees showed that they were receiving an average of e-mails per day. The computer server through which the e-mails are routed showed that Has the new policy had any effect? Use a 10% level of significance to test the claim that there has been a change (either way) in the average number of e-mails received per day per employee. If the P-value for the data is 0.015, are the data statistically significant at level Based on your answers, will you reject or fail to reject the null hypothesis?

a)Since the P-value is greater than the level of significance, the data are statistically significant. Thus, we fail to reject the null hypothesis.

b)Since the P-value is less than the level of significance, the data are statistically significant. Thus, we fail to reject the null hypothesis.

c)Since the P-value is less than the level of significance, the data are not statistically significant. Thus, we reject the null hypothesis.

d)Since the P-value is less than the level of significance, the data are statistically significant. Thus, we reject the null hypothesis.

e) Since the P-value is less than the level of significance, the data are not statistically significant.

30.How much should a healthy Shetland pony weigh? Let x be the age of the pony (in months), and let y be the average weight of the pony (in kilograms). Suppose a random sample of ponies gave the following information.

Compute r.

a)0.020

b)0.995

c)–0.995

d)–0.020

e)none of these choices

31.It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) for an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. Suppose that the following data were obtained for a collection of archaeological sites in New Mexico:

Find a for the equation of the least-squares line

a)0.042

b)–0.042

c) 0.123

d) –0.056

e) 16.117

32.The following table shows the Myers-Briggs personality preferences for a random sample of 410 people in the listed professions.

Use the chi-square test to determine if the listed occupations and personality preferences are independent at State the null and alternate hypotheses.

a) Myers-Briggs preference is independent whereas profession is not independent; Myers-Briggs preference is not independent whereas profession is independent

b) Myers-Briggs preference and profession are independent; Myers-Briggs preference is not independent whereas profession is independent

c) Myers-Briggs preference is not independent whereas profession is independent; Myers-Briggs preference and profession are independent

d) Myers-Briggs preference is independent whereas profession is not independent; Myers-Briggs preference and profession are not independent

e) Myers-Briggs preference and profession are independent; Myers-Briggs preference and profession are not independent