Ch. 5 Normal Distribution
For the first group of questions - use your half sheet on the 68-95-99.7 Rule (Empirical Rule).
A new group of IQ tests are standardized to a Normal Model, N(110,14).
Answer:
What percent of the data values fall between the IQ's of 96 and 124?
What does the z-score mean?
Suppose that a Normal model described student scores in a history class.
Francisco has a standardized score (z-score) of +2.5.
This means that Francisco’s score...
If the heights of 6th graders at Danville Middle School follow a normal distribution with the mean height of 58.5 inches and the standard deviation of 2.45 inches, give the notation for the Normal model.
Use the format: N(mean, std dev)
High levels of cholesterol in the blood increase the risk of heart disease. For teenage boys, the distribution of blood cholesterol is approximately normal with mean μ = 151.6 milligrams of cholesterol per deciliter of blood (mg/dl) and standard deviation σ = 25 mg/dl.
What is the Normal model for this situation?
Use the format: N(mean, std. dev.)
People with z-scores greater than 2.5 on an IQ test are considered as geniuses.
IQ tests have a score of a mean of 100 and SD of 16 points.
What is the cut off score to show someone is a genius? Hint: use the z-score.
Chapter 6 Sampling Distributions
A study of voting chose 663 registered voters at random shortly after an election. Of these, 72% said they had voted in the election. Election records show that only 56% of registered voters voted in the election.
Match up the following statements about these percentages?
| Draggable item | arrow_right_alt | Corresponding Item |
|---|---|---|
663 regsitered voters | arrow_right_alt | Parameter |
56% | arrow_right_alt | Statistic |
All voters | arrow_right_alt | Sample |
72% | arrow_right_alt | Population |
Vermont is particularly beautiful in early October when the leaves begin to change color. At that time of year, a large proportion of cars on Interstate 91 near Brattleboro have out-of-state license plates.
Suppose a Vermont state trooper randomly selects 50 cars driving past Exit 2 on I-91, records the state identified on the license plate, and calculates the proportion of cars with out-of-state plates.
What is the Vermont state trouper recording?
Which of the following describes the sampling distribution of the sample proportion in this context?
A polling organization wants to estimate the proportion of voters who favor a new law banning smoking in public buildings.
The organization decides to increase the size of its random sample of voters from about 1500 people to about 4000 people right before an election.
The effect of this is to
The central limit theorem is important in statistics because it allows us to use the normal distribution to find probabilities involving the sample mean if the
Scores on the mathematics part of the SAT exam in a recent year followed a normal distribution with mean 515 and standard deviation 114.
You choose an SRS of 100 students and calculate mean SAT Math score.
Match up the following for this situation.
| Draggable item | arrow_right_alt | Corresponding Item |
|---|---|---|
11.4 | arrow_right_alt | sample size (n) |
100 | arrow_right_alt | |
515 | arrow_right_alt | |
114 | arrow_right_alt |
Use the information in the previous question.
What is the probability of getting a sample of 100 registered voters with more than 65% democrats?
Keep all decimals.
Using the information above, suppose an actual sample of 100 of the registered voters actually resulted in 65% democrats. Would you have convincing evidence that the estimated 52% democrat voters was incorrect? Explain.
Use the information from the previous question:
What is the shape of the population and the sampling distribution of x-bar ? Justify.
Chapter 7: Confidence Intervals
Tim purchased a random sample of clementines at a local grocery store. The 95% confidence interval for the mean weight of all clementines at this store is 76.6 grams to 90.1 grams. Interpret this confidence interval.
Based on your previous answer:
Explain what the confidence interval tells you about whether the national value of 73% holds at this university.
Based on your previous answer:
Explain what the confidence interval tells you about whether the manager's requirement of 40 pepperonis on each large pizza is being followed.
The puzzle editor of a game magazine asked 43 randomly selected subscribers how long it took them to complete a certain crossword puzzle. The 99% confidence interval for the median completion time for all subscribers is 15.2 to 18.6 minutes.
Explain what would happen to the length of the interval if the sample size were increased to 200 students.
The puzzle editor of a game magazine asked 43 randomly selected subscribers how long it took them to complete a certain crossword puzzle. The 99% confidence interval for the median completion time for all subscribers is 15.2 to 18.6 minutes.
Explain what would happen to the length of the interval if the confidence level were increased to 99%.
Chapter 8
Identify the types of Errors when performing a significance test:
Ha is TRUE and you REJECT Ho
Ho is TRUE and you REJECT Ho
Ho is TRUE and you FAIL TO REJECT Ho
Ha is TRUE and you FAIL TO REJECT Ho
Type I Error
Type II Error
No Error
Flu vaccine A drug company has developed a new vaccine for preventing the flu. The company claims that less than 5% of adults who use its vaccine will get the flu. To test the claim, researchers give the vaccine to a random sample of 1000 adults. Of these, 43 get the flu.
Ho: p > 0.05
Ha: p < 0.05
What is a Type I Error in this setting?
What is a Type II Error in this setting?
Which would be a more serious mistake in this setting—a Type I error or a Type II error?
Deciding that 5% or more of adults who use the vaccine will get the flu, so the vaccine is not used and less than 5% will actually get the flu.
Deciding that less than 5% of adults who use the vaccine will get the flu, so the vaccine is used and 5% or more will actually get the flu.
Deciding that 5% or more of adults who use the vaccine will get the flu so the vaccine is not used and 5% or more will actually get the flu.
Deciding that less than 5% of adults who use the vaccine will get the flu and less than 5% actually get the flu.
Type I Error
Type II Error
A college president says, “More than two-thirds of the alumni support my firing of Coach Boggs.” The president’s statement is based on 200 emails he has received from alumni in the past three months.
The college’s athletic director wants to perform a test of
H0: p = 2/3 versus Ha: p > 2/3, remember: 2/3 = 0.667
where p = the true proportion of the college’s alumni who favor firing the coach.
Have the conditions been met for calculating a significance test?
Select all correct answers:
What is the conclusion based on the P value above?
Based on an alpha level of 0.10, give the conclusion for the significance test.