Parameter
Measures something in the population
Statistic
Measures something in the sample
Law of Large Numbers
As the number of observations taken increases, the mean x of the observed value gets closer and closer to the mean ? of the population
Central Limit Theorem
When n is large, the sampling distribution of the sample mean x is approximately normal.
Binomial Distributions
The distribution of the count X successes in the binomial experiment with parameters n and p.
n
number of observations
p
probability
q
1-p
Statistical interference
Provides methods for drawing conclusions about a population from sample data
Population Standard Deviation
?
Population Mean
?
Sample Mean
x?
Confidence Intervals
The interval of numbers between the values of x?
Null Hypothesis
H0
Alternative Hypothesis
Ha
Test Statistic
Standardized value that is calculated from sample data during a hypothesis test
P-value
The probability of obtaining a result equal to or "more extreme" than what was actually observed, when the null hypothesis is true
Significance levels
Fixed standards for P-value represent by ?
Degrees of Freedom
Statistical wiggle room
Critical Values
Test values
Two-way table
Organize data based on two categorical variables
Chi-Square Statistical Tests
Used to determine if there is a relationship between observed results and expected results
Expected count
(Row Total)(Column Total)/Table Total
Sale of eggs that are contaminated with salmonella can cause food poisoning among consumers. A large egg producer takes an SRS of 200 eggs from all the eggs shipped in one day. The laboratory reports that 11 of these eggs had salmonella contamination. Unk
A. 0.2% is a parameter and 11 is a statistic.
Previous studies have suggested that the average weight of a particular animal species is 121.3 pounds with a standard deviation of 20.9 pounds. The distribution is just about normal.
1. A sample of 90 of these animals is taken. What is the sampling distr
1. N (121.3, 2.2)
2. 0.0021
The Central Limit Theorem is important in statistics because it allows use to use the Normal Distribution to make inferences concerning the population mean
B. if the population is Normally distributed and the sample size is reasonably large
The mean income of a sample of 98,000 houses contacted by a survey company was x? = $66,570. The monetary value is a
C. Statistic
A professional golfer drives 25 balls off a tee, an electric timer measuring ball speed off the tee shows a mean speed of 173.5 mph with a standard deviation of 2.4 mph. Assume the golfer never tires and there is consistent Normal distribution of ball spe
1. 0.0721
2. Extremely close to 0
The law of large numbers states that as the number of observations drawn at random from a population with finite mean ? increases, the mean x? of the observed values:
C. Tends to get closer and closer to the population ?
Which symbol is used to represent sample mean?
x?
Which symbol is used to represent population standard deviation?
?
The incomes in a certain large population of college teachers have a normal distribution with mean $75,000 and standard deviation $10,000. Four teachers are selected at random from this population to serve on a committee. What is the probability that thei
0. 1587
Incomes in a certain town are fairly Normal with a mean of $36,000 and a standard deviation of $7000. A random sample of 75 households is taken. What is the probability the sample mean is greater than $37,000?
0.1075
I took a large sample of households in a city, and based on that, estimate the standard deviation of the income for all households in the city is $800. In order to make a desired conclusion about the income for all the households in the city, I want the s
64
In a large population of college-educated adults, the mean IQ is 112 with standard deviation 25. Suppose 300 adults from this population are randomly selected for a market research campaign. the probability that the sample mean IQ is greater than 115 is:
B. Approximately Normal with mean 112 and standard deviation 1.443
The average study rime for a final exam in History is found to be 6.5 hours with a standard deviation of 1.75 hours. Assume the distribution is Normal. What is the probability that a student chosen at random spends more than 7 hours in studying?
0.2857
According to the distribution above, what is the probability that a student chosen at random spends less than 9 hours in studying?
0.9236
A roulette wheel has 38 slots in which the ball can land. Two of the slots are green, 18 are red, and 18 are black. The ball is equally likely to land in any slot. The roulette wheel is going to be spun twice and the outcomes of the two spins are independ
1. A. 0.0249
2. B. 0.7230
A survey of college students finds that 20% like country music, 15% like gospel music, and 10% like both country music and gospel music.
1. The proportion of students who like gospel music but not country music is:
2. The proportion of students that like
1. A. 5%
2. C. 75%
3. D. 25%
4. B. Approximately 66.7%
The following table gives the sex and age group of college students at a Midwestern university.
A student is to be selected at random.
1. The probability that the selected student is 25 to 34 years old is:
2. The probability that the selected student is a
1. A. 0.210
2. A. 0.005
3. B. 0.204
In a particular game, a fair die is tossed. If the number of spots showing is a six, you win $6, if the number of spots showing is a five, you win $3, if the number of spots showing is 4, you win $2, and if the number of spots showing is 3, you win $1. If
C. 4/9
An event A will occur with probability 0.5. An event B will occur with probability 0.6. The probability that both A and B will occur is 0.1. We may conclude:
B. Either A or B always occurs
Explain what mutually exclusive means
They cannot occur at the same time.
A psychology instructor asked the 100 females in her class to rate their intelligence on a scale of 1 to 10.
What is the probability that a student rated herself an 8, given that she rated herself at least an 9?
0.6
A salesman makes visits to customers. Based on his past history, the probability he makes a sale on any visit is 0.15. It is reasonable to assume that customers' decisions are independent of one another. If he makes 10 visits in a day, what is the chance
0.0098
There are five multiple-choice questions on an exam, each having responses a, b, c, or d. Each question is worth five points and only one option per question is correct. Suppose the student guesses the answer to each question, and the guesses from questio
1.25
As part of a promotion for a new type of cracker, free samples are offered to shoppers in a local supermarket. The probability that a shopper will buy a package of crackers after tasting the free sample is 0.2. Different shoppers can be regarded as indepe
1.789
From previous polls, it is believed that 66% of likely voters prefer the incumbent. A new poll of 500 likely voters will be conducted. In the new poll, if the proportion favoring the incumbent has not changed, what is the mean and standard deviation of th
? = 330, ? = 10.59
In an instant lottery, your chances of winning is 0.1. If you play the lottery 5 times and the outcomes are independent, the probability that you win at most once is:
C. 0.919
As part of a promotion for a new type of cracker, free samples are offered to shoppers in a local supermarket. The probability that a shopper will buy a package of crackers after tasting the free sample is 0.2. Different shoppers can be regarded as indepe
0.0052
Ladies Home Journal magazine reported that 66% of all dog owners greet their dog before greeting their spouse or children when they return home at the end of the workday. Assume that this claim is true. Suppose 12 dog owners are selected at random. Let X
1. ? = 7.92, ? = 1.64
2. 1 - bimomcdf (12, 0.66, 6)
3. 0.0038
In an instant lottery, your chances of winning is 0.1. If you play the lottery 5 times and the outcomes are independent, the probability that you will lose all 5 times is:
B. 0.590
If X has a binomial distribution with 20 trials and a mean of 6, the the success probability p is:
A. 0.30
At a large Midwestern college, 4% of the students are the same race as Andr�s Recalde. A random sample of 20 students from the college are selected. Let X denote the number of Hispanics among them. What are the mean and standard deviation of X?
? = 0.8, ? = 0.876
What is the rule concerning Normal Approximation?
It has to be greater than 10.
How do you find the binomial coefficient?
Math > Prb > nck
You are calculating a confidence interval at the 99& confidence level. For your data, ? = 8. What does the sample have to be for the margin of error to be 5?
n = 17
The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitude toward school, and study habits of students. Scores range from 0 to 200. The mean score for U.S. college students is about 115, and the standard
1. (111.56, 124.44)
2. (113.89, 122.11)
A guidance counselor wishes to determine the
mean number of changes in academic major by
college students to within �0.1 at a 90 percent
confidence level. What sample size should be
chosen if it is known that the standard deviation is
0.45?
n = 55
Suppose we want a 90% confidence interval for the average amount spent on books by freshman in their first year at a major university. The interval is to have a margin of error of $2, and the amount spent has a Normal distribution with a standard deviatio
d. 609
The National Assessment of Educational Progress ( NAEP) includes a mathematics test for high school seniors. Scores on the test range from 0 to 300. Suppose that you give the NAEP test to an SRS of 900 12th-graders from a large population in which the sco
1.16
In a recent Zogby International survey, 11% of 10,000 Americans under 50 said they would be willing to implant a device in their brain to be connected to the internet if it could be done safely. What is the margin of error at the 99% confidence interval?
E. 2.576 � ? (0.11)(0.89)/10,000
In an SRS of 50 teenagers, two-thirds said they would rather text a friend than call. What is the 98% confidence interval for the proportion of teens who would rather text than call a friend?
B. 2/3 � 2.326 ? (2/3)(1/3)/50
A candidate for one of Ohio's two U.S. Senate seats wishes to compare her support among registered voters in the northern half of the state with her support among registered voters in the southern half of the state. A random sample of 2000 registered vote
(0.05012, 0.11188)
In a large midwestern university (the class of entering freshmen is 6000 or more students), an SRS of 100 entering freshmen in 1999 found that 20 finished in the bottom third of their high school class. Admission standards at the university were tightened
D. -0.029 to 0.229
An SAT prep class of 30 (use t-interval) randomly selected students produces the following improvement in scores
1. Calculate a 90% confidence interval for the mean improvement in test scores
2. If you find a confidence interval for the mean improvement i
1. (50.621, 75.779)
2. The interval will widen.
What is the critical t-value for finding a 90% confidence interval from a sample of 18 observations?
1.74
What is the critical t-value for finding a 90% confidence interval from a sample of 15 observations?
A. 1.761
A study is undertaken to determine the proportion of industry executives who believe that workers' pay should be based on individual performance. How many executives should be interviewed if an estimate at the 99% confidence level to within �.03?
1,844
Suppose that 84% of a sample of 125 nurses working 7 AM to 3 PM shifts in city hospitals express positive job satisfaction, while only 72% of a sample of 150 nurses on 11 PM to 7 AM shifts express similar fulfillment.
1. Establish a 90% confidence interva
1. (0.0391, 0.2009)
2. 0.0809
In formulating a hypothesis for a statistical test of significance H0:
C. A statement of no difference or no effect
In their advertisements, the manufacturers of a certain brand of oatmeal would like to claim that eating their oatmeal for breakfast daily will produce a mean decrease in
cholesterol of more than 10 points in one month for people with cholesterol levels o
A. Ha: ? > 10
The mean area ? of the several thousand apartments in a new development by a certain builder is advertised to be 1100 square feet. A tenant group thinks this is inaccurate, and suspects that the actual average area is less than 1100 square feet. In order
B. H0: ? = 1100 and Ha: ? < 1100.
Is the mean age at which American children can first read now under 4 years? If the population of all American children has mean age of � years until they begin to read and standard deviation ? years, one would test which of the following null and alterna
B. H0 : � = 4 v.s. Ha : � < 4.
The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitude toward school, and study habits of students. Scores range from 0 to 200 and follow a Normal distribution, with mean = 110 and standard deviation
p = 0.0586
The level of calcium in the blood of healthy young adults follows a normal distribution, with mean � = 10 milligrams per deciliter and standard deviation � = 0.4. A clinic measures the blood calcium of 25 healthy pregnant young women at their first visit
1. A. less than 0.0002
2. I would reject H0 based on a significance level of 0.1.
Suppose the time that it takes a certain large bank to approve a home loan is normally distributed with mean (in days) ? and standard deviation ?= 1. The bank advertises that it approve loans in 5 days, on average, but measurements on a random sample of 5
D. Null hypothesis should be rejected
The time needed for college students to complete a certain paper and pencil maze follows a Normal distribution with a mean of 80 seconds and a standard deviation of 16 seconds. You wish to see if the mean time ? is changed by meditation, so you have a gro
B. H0 should not be rejected
A long accepted measure of the discharge rate (in 1000 ft3/sec) at the mouth of the Mississippi River is 593. To test if this has changed, ten measurements at random times are takenL 590, 596, 592, 588, 594, 590, 586, 591, 589. State the H0, Ha, and state
H0 = 593
Ha ? 593
Based on a significance level of 0.1, H0 should be rejected.
Recent revenue shortfalls in a southern state led to a reduction in the state budget for higher education. To offset the reduction, the largest state university proposed a 20% tuition increase. It was determined that such an increase was needed to simply
1. 61
2. 43.88
3. p = 0.000000001597
A random sample of Ohio voters was asked about the number of cars or trucks they own and the type of community they lived in.
1. What are the degrees of freedom?
2. What is the expected number of suburban residences with two cars?
3. The chi-square statis
1. df = 4
2. 588
3. B. Less than .01
To study the export activity of manufacturing firms in Korea, questionnaires were mailed to an SRS of firms in each of three industries that export many of their products. The response rate was low, and to compare the industries it is important that the r
A. Is greater than 0.05
A study examines the personal goals of children in grades 4, 5, and 6. A random sample of students was selected for each of the grades 4, 5, and 6 from schools in Georgia. The students received a questionnaire regarding achievement of personal goals. They
179.93
There is intense competition among internet service providers to get their home customers to switch from dial up to high speed broadband service. In 2006, a survey of 1758 randomly selected U.S. households was conducted. This survey was then compared to a
D. At the 10% level of significance, we can conclude that the rate of broadband use across income levels has changed between 2005 and 2006.
A company has been running television commercials for a new children's product on five different family programs. A random sample of families is taken.
What would be the degrees of freedom for this test?
C. 12