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?
Required
3 points
3
Question 2
2.
Using the Normal Distribution from #1:
How many standard deviations from the mean is the top 16% of the IQ scores? _______
What is the IQ score needed to be in the top 16%? _______
What percentile would this be? _______
Hint: remember, percentiles are the percent to the LEFT of a given point
Then shade the corresponding area under the normal curve in the 'show your work' area below.
Required
3 points
3
Question 3
3.
Using the Normal Distribution from #1:
How many standard deviations is the top 2.5% from the mean? _______
What is the IQ score needed to be in the top 2.5%? _______
What percentile would this be? _______
Hint: remember, percentiles are the percent to the LEFT of a given point
Then shade the corresponding area under the normal curve in the 'show your work' area below,.
Required
3 points
3
Question 4
4.
Using the Normal Distribution from #1:
What percent of the IQ scores are 82 or lower? _______
What percent of the IQ scores are 124 or lower? _______
What percent of the IQ scores are 68 or lower? _______
Hint: remember, percentiles are the percent to the LEFT of a given point
Required
2 points
2
Question 5
5.
Fill in the blanks:
Using the normal distribution model:
N(3.25, 1.4) Mean= _______ Standard Deviation= _______
Required
1 point
1
Question 6
6.
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...
Required
1 point
1
Question 7
7.
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)
Required
2 points
2
Question 8
8.
The Delorean speeds from 'Back To The Future' follow a Normal Distribution, with the model N(80, 7.7).
What percent of the runs will give the Delorean a speed less than 68.45 mph?
First: what is the z-score for 68.45? _______ Enter all decimal places for this one.
Use the z-score formula:
Second: answer,
what is the proportion of runs that will give the Delorean a speed less than 68.45 mph? _______
THEN: Shade in the probability area that you are calculating in the 'show your work' area.
Required
4 points
4
Question 9
9.
What percent of the runs will give the Delorean a speed greater than 85 mph?
First: what is the z-score for the speed? _______
Remember to round to two places.
Second: be careful, I am asking for the percent GREATER than 85 mph, think about what you need to do, collaborate!
What is the proportion of speeds less than 85 mph? _______
Third: What do you need to do with the value to find the proportion higher?
Add, subtract, multiply or divide? _______
What percent of the runs will give the Delorean a speed greater than 85 mph? _______
Hint: the area to the left and the right need to add to 1.0, the total area under the curve.
THEN: Shade in the probability area that you are calculating in the 'show your work' area.
Required
6 points
6
Question 10
10.
What percent of the runs will give the Delorean a speed between 70 and 95 mph?
Remember it follows the model: N(80, 7.7).
First: what is the z-score for the speed of 70 mph? _______
Remember to round to two places.
what is the z-score for the speed of 95 mph? _______
Second: what proportion corresponds to 70 mph? _______
what proportion corresponds to 95 mph? _______
Third: answer, what will you do with the two proportions?
Add, subtract, multiply or divide? _______
What percent of the runs will give the Delorean a speed between 70 and 95 mph? _______
Hint: you want the area BETWEEN the two points, you will need to subtract!
THEN: Shade in the probability area that you are calculating in the 'show your work' area.
Required
1 point
1
Question 11
11.
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.)
Required
2 points
2
Question 12
12.
What proportion of teen boys have cholesterol levels less than 100 mg/dl?
First: what is the z-score for 100 mg/dl? _______ Remember to round to two places.
Second: What is the proportion? _______
THEN: Shade in the probability area that you are calculating in the 'show your work' area.
Required
4 points
4
Question 13
13.
Cholesterol levels of 200 or higher are considered high for teenagers.
What percent of teen boys have high cholesterol?
First: what is the z-score for 200 mg/dl? _______
Second: What is the proportion to the left of the z-score? _______
What do you need to do with the value to find the proportion higher?
Add, subtract, multiply or divide? _______
Third: what is the proportion GREATER than 200 mg/dl? _______
THEN: Shade in the probability area that you are calculating in the 'show your work' area.
Required
6 points
6
Question 14
14.
Cholesterol levels between 170 mg/dl and 200 mg/dl are considered borderline high for teenagers. What percent of teen boys have borderline high cholesterol levels?
First: what is the z-score for 170 mg/dl? _______
what is the z-score for 200 mg/dl? _______
Second: What is the proportion to the left of 170? _______
What is the proportion to the left of 200? _______
Third: what will you do with the two proportions? Add, subtract, multiply or divide? _______
what percent of teen boys have borderline high cholesterol levels? _______
THEN: Shade in the probability area that you are calculating in the 'show your work' area.
Required
1 point
1
Question 15
15.
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.
Required
4 points
4
Question 16
16.
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
72%
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Parameter
All voters
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Statistic
663 regsitered voters
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Sample
56%
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Population
Required
2 points
2
Question 17
17.
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?
Required
2 points
2
Question 18
18.
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
Required
2 points
2
Question 19
19.
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
Required
3 points
3
Question 20
20.
At a high school, 85% of students are right-handed.
Let X = the number of students who are right-handed in a random sample of 10 students from the school.
What is the sample size? n= _______
What is the mean of the sampling distribution? _______ enter as a proportion, not a percent.
What is the standard deviation of the sampling distribution? _______ Round to three places past the decimal point.
Required
4 points
4
Question 21
21.
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
515
arrow_right_alt
sample size (n)
114
arrow_right_alt
100
arrow_right_alt
11.4
arrow_right_alt
Required
3 points
3
Question 22
22.
In a congressional district, 52% of the registered voters are Democrats. An SRS of 100 voters is going to be polled.
What is the mean of the sampling distribution of the sample proportion of democrat voters? _______
What is the standard deviation of the sampling distribution of the sample proportion of democrat voters? _______ Round to two places past the decimal.
What is the probability of getting less than 50% Democrats in a random sample of size 100?
_______
Keep your answer as the decimal proportion, keep all decimal places (there will be four)
Required
1 point
1
Question 23
23.
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.
Required
4 points
4
Question 24
24.
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.
Required
2 points
2
Question 25
25.
The amount that households pay service providers for access to the Internet varies quite a bit, but the mean monthly fee is $48 and the standard deviation is $20.
The distribution is not normal: Many households pay a base rate for low-speed access, but some pay much more for faster connections so the distribution is strongly right skewed.
A sample survey asks an SRS of 500 households with Internet access how much they pay per month. Let X-bar be the mean amount paid by the members of the sample.
Calculate the mean and standard deviation of the sampling distribution of the sample means.
Sampling distribution sample mean = _______
Sampling distribution of sample means standard deviation = _______
Round to three places past the decimal.
Required
3 points
3
Question 26
26.
Use the information from the previous question:
What is the shape of the population and the sampling distribution of x-bar ? Justify.
Required
2 points
2
Question 27
27.
Use the information in the previous two questions:
In a sampling distribution, find the probability that the average amount paid by the sample of households exceeds $50.
z-score = _______ round to two places past the decimal
Probability = _______ Keep the probability as a decimal proportion
Required
2 points
2
Question 28
28.
Use the information from the previous 3 questions:
In a sampling distribution, what is the probability that the average amount paid by the sample of households is less than $46.50.
z-score = _______ round to two places past the decimal
Probability = _______ Keep your answer as a decimal proportion.
Required
1 point
1
Question 29
29.
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.
Required
2 points
2
Question 30
30.
In a recent year, 73% of first-year college students identified “being very well-off financially” as an important personal goal.
A state university finds that 132 of an SRS of 200 of its first-year students say that this goal is important.
Construct a 95% confidence interval for the true proportion of all first-year students at the university who would identify being well-off as an important personal goal.
Check your formula chart, round to three places past the decimal.
Lower bound: _______
Upper bound: _______
Required
2 points
2
Question 31
31.
Based on your previous answer:
Explain what the confidence interval tells you about whether the national value of 73% holds at this university.
Required
2 points
2
Question 32
32.
Melissa and Madeline love pepperoni pizza, but sometimes they are disappointed with the small number of pepperonis on their pizza.
To investigate, they went to their favorite pizza restaurant at 10 random times during the week and ordered a large pepperoni pizza. Here are the number of pepperonis on each pizza.
47 36 25 37 46 36 49 32 32 34
Statsmedic.com gives an average of 37.4 pepperonis and a Sx= 7.662
Construct and interpret a 95% confidence interval for the true mean number of pepperonis on a large pizza at this restaurant.
Check your formula chart, round to three places past the decimal.
Lower bound: _______
Upper bound: _______
Required
2 points
2
Question 33
33.
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.
Required
2 points
2
Question 34
34.
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.
Required
2 points
2
Question 35
35.
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%.
Required
4 points
4
Question 36
36.
Chapter 8
Identify the types of Errors when performing a significance test:
Ho is TRUE and you FAIL TO REJECT Ho
Ha is TRUE and you REJECT Ho
Ha is TRUE and you FAIL TO REJECT Ho
Ho is TRUE and you REJECT Ho
Type I Error
Type II Error
No Error
Required
2 points
2
Question 37
37.
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 less than 5% of adults who use the vaccine will get the flu and less than 5% 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.
Type I Error
Type II Error
Required
3 points
3
Question 38
38.
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:
Required
4 points
4
Question 39
39.
Zenon decided to investigate whether students at his school prefer name-brand potato chips to generic potato chips. He randomly selected 50 students and had each student try both types of chips, in random order.
Overall, 34 of the 50 students preferred the name-brand chips.
Zenon wants to perform a test at the α = 0.05 significance level of
H0: p = 0.5 versus Ha: p > 0.5,
where p = the true proportion of all students at his school who prefer name-brand chips.
Sample proportion = _______
Sampling distribution standard error = _______ round to three places past the decimal
Standardized test statistic (z statistic) = _______ round to two places past the decimal
What is the p value for having this sample proportion given the null value is true? _______ Keep all places past the decimal.
Required
3 points
3
Question 40
40.
What is the conclusion based on the P value above?
Required
5 points
5
Question 41
41.
Suppose that you want to perform a test at the α = 0.10 significance level of
H0 : μ = 5
Ha: μ ≠ 5
A random sample of size n = 20 from the population of interest yields mean= 5.21 and
Sx = 0.79.
Calculate the standard error for the sampling distribution: _______ round to 3 places past the decimal
Calculate the standardized test statistic: _______ round to 3 places past the decimal
Degrees of freedom = _______
Give the lower and upper probabilities for the P-value interval: _______ - _______
Required
1 point
1
Question 42
42.
Based on an alpha level of 0.10, give the conclusion for the significance test.