Stat 100 final
Customers at a Bakery spend an average of $15 with a median of $5 and a standard deviation of $10. What is the standard deviation of the average amount spent by the next 25 customers?
$2
Use the information below to answer the two questions that follow: 200 randomly selected adult females and 200 randomly selected adult males were checked for high blood pressure. The collected data is summarized in the following contingency table. What is the relative risk of high blood pressure when comparing males to females.
(80/200)/(50/200) = 1.6
The width of the nests of house finches average 5 inches with a standard deviation of 0.8 inches and approximately follow the normal distribution.What percentage of these birds' nests are more than 4inches across?
- empirical rule -z= 4-5/.8 =-1.25 -from the tables, this z is between the 10th and 11th percentile so the answer is between 89% and 90% (but subtract from 100)
In the water pollution poll example, where the sample proportion was 0.61 and the sample size was n=1019, the standard error is what. Give your answer as a decimal.
.015
The standard error for the proportion of smokers with wrinkles is what?
.0394
•Suppose that 30% of Penn State students are from Philadelphia county. We are going to simulate taking repeated samples of size n=100 from the Penn State student population, and computing the proportion of these samples that are from Phila county. This question is based on the stat key simulation activity: What is the standard deviation of the sampling distribution?
.045
A random sample of 100 freshmen students at University Park campus is taken to estimate the percentage of freshmen that have taken a tour of Pattee Library during orientation week. Of the 100 freshmen, 40 (40%) of them have taken a tour of Pattee Library. The standard error (SE) for a sample proportion in this situation is estimated to be approximately:
.049
An airline that flies from Pittsburgh, Pennsylvania to Denver, Colorado finds that thirty percent of the passengers on this route take advantage of steep discounts (early buyer discounts, frequent flyer discounts, etc...), thirty-five percent pay the regular economy fare, thirty percent pay the business class fare, and the remaining pay the first class fare. What is the probability that a randomly selected passenger pays the first class fare? Give your answer as a decimal or proportion.
.05
The next two questions are based on the following: Twenty percent (20%) of American adults take part in some kind of betting pool for the March Madness NCAA basketball tournament. In a random sample of 64 American adults, the standard deviation of the proportion of the sample that has taken part in a March Madness pool would be about:
.05
•Suppose the true average IQ for PA residents is 100, with a standard deviation of 16. Suppose I take a sample of 64 PA residents. What is the chance that the average IQ of this sample is larger than 103. Give your answer as a decimal.
.07
Suppose that 68% of Penn State students were born in PA. I am interested in taking samples of 36 students, and calculating the proportion of the sample that is was born in PA. What is the standard deviation of the distribution of the proportion of students in the sample that were born in PA? Answer to 3 decimal places.
.078
Customers at a Bakery spend an average of $15 with a median of $5 and a standard deviation of $10. What is the standard deviation of the proportion of the next 25 customers that will spend over $5?
.1
Suppose that 30% of Penn State students are from Philadelphia county. We are going to simulate taking repeated samples of size n=100 from the Penn State student population, andcomputing the proportion of these samples that are from Phila county. What is the chance that more than 36% of a sample of 100 students are from Phila county. Give your answer as a proportion.
.11
Suppose in the same scenario I instead take a sample of only 9 students. What would the new standard deviation be? Answer to 3 decimal places.
.155
In a random sample of 64 American adults, the chance that at least 16 of them will have taken part in a March Madness pool would be about:
.16
Twenty percent of the cars on the road in one state are four-wheel drive. What is the chance that at least 22% of a group of 400 randomly selected cars from that state have four-wheel drive? Give your answer as a decimal between 0 and 1.
.16
The average household income is 64,000. The standard deviation of household incomes is about $30,000. You pick a random sample of 50 households. What is the chance the average household income in your sample is under $60,000? Give the answer as a decimal.
.17
Overnight packages shipped by FedEx to one city weigh an average of 5 ounces with a standard deviation of 6 ounces. What is the chance that the next 100 packages weigh a total of between 480 and 520 ounces? Give the answer as a number between 0 and 1.
.26
When making a 95% confidence interval in the veteran's health care example, the upper bound of the confidence interval is what? Give your answer as a decimal.
.294
Seventy percent of the customers at a gas station pay by credit card. Others by pay by either cash or check. What's the chance that the next customer will pay by cash or check?
.3
A soda machine sells Coke, Diet Coke, Sprite, and Root Beer. Thirty percent of the customers who use this machine buy Diet Coke, 20% buy Sprite, and 10% buy Root Beer. What is the probability that a randomly selected customer buys Coke?
.4
Customers at a Bakery spend an average of $15 with a median of $5 and a standard deviation of $10. What is the chance the next customer spends over $5?
.5
The amount of gas purchased by customers at a gas station averages 12 gallons with a standard deviation of 5 gallons. Suppose I am interested in the average amount of gas purchased by the next 100 customers. What is the standard deviation of the distribution of the average amount of gas purchased by the next 100 customers? (Look at slide 20 or the link in the announcement.)
.5
- In the 2016 Presidential Election, Donald Trump received 48% of the vote in Pennsylvania. On the day of the election you take a random sample of 100 Pennsylvania voters after they voted. What is the probability that a majority of your sample did not vote for Trump? Give your answer as a decimal.
.65
A random sample of 100 freshmen students at University Park campus is taken to estimate the percentage of freshmen that have taken a tour of Pattee Library during orientation week. Of the 100 freshmen, 40 (40%) of them have taken a tour of Pattee Library. An 80% confidence interval for the proportion of all freshmen who took the tour would then be:
0.4 ± 0.06
Reese's Pieces candies come in three colors: yellow, orange and brown. Half of all Reese's Pieces are orange and twenty-five percent are brown. One Reese's Pieces candyis chosen at random. The odds thatit is orange are
1 to 1
Back to the original scenario where the sample size is 36, suppose I want to know the probability that more than 30 students in the sample are from PA. If 30 students in the sample are from PA, then what is the corresponding z-score for this value. Hint: first convert to a proportion, then use the mean and standard deviation from the first two questions.
1.97 (margin .09)
I roll a 6 sided die twice. What is the probability I roll a 6 both times?
1/36
You roll a fair six-sided die and the die lands with a 3 face up. What is the probability that a second roll also results in a 3?
1/6 because the two rolls do not influence each other.
In the German GPA example, what percentage of students have a GPA of less than 70%
13%
For a fair coin, what is the chance of getting at least 15 heads in 25 tosses?
16%
Another new metacarpal bone is found that is only 20 mm long (probably coming from a child instead of anadult skeletonlike thosethat make up the ten in the data set above). Can you use the regression output above to estimate the height of that skeleton? If so, make the estimate. If not, explain briefly why you can't.
20 is well outside the range of data so its not legit to predict a skeleton heigh for that a child's skeleton may not fit the same pattern as for the data from adults
In the diameter of Jupiter example, what is the margin of error when making the 95% confidence interval for the true diameter of Jupiter?
24
Reese's Pieces candies come in three colors: yellow, orange and brown. Half of all Reese's Pieces are orange and twenty-five percent are brown. One Reese's Pieces candyis chosen at random. The chance it is yellow is
25%
Reese's Pieces candies come in three colors: yellow, orange and brown. Half of all Reese's Pieces are orange and twenty-five percent are brown. Two Reese's Pieces candies are chosen at random. The chance they are both orange is
25%
If 100 homes had been randomly selected instead of 400, then the chance that the percent of homes in the sample that have a bank mortgage is between 76% and 80% would be about
34%
What is the probability that the next two customers both buy Sprite?
4% because the customers choices would be independent
Eighty percent of the single-family homes in a large city have a bank mortgage. 400 homes are randomly selected from the city. The chance that the percent of homes in the sample that have a bank mortgage is between 76% and 80% is about
48%
The monthly mortgage payments made to a credit union have a median of $2150 with a mean of $2520 and a standard deviation of $1130. What percentage of the monthly mortgage payments are at least $2150?
50
What is the increased risk of high blood pressure when comparing males to females.
60%
15. The director of admissions in a small college administered a newly designed entrancetest to 100 students selected at random from the upcoming freshman class. The purposeof this study was to determine whether students' grade point average (GPA) at theend of the freshman year can be predicted from the entrance test score. At the end ofthe year when all the data are available, what would be the graph you would use todisplay the data?
A scatterplot with GPA on the y-axis and the entrance test scores on the x-axis.
The director of admissions in a small college administered a newly designed entrance test to 100 students selected at random from the upcoming freshman class. The purpose of this study was to determine whether students' grade point average (GPA) at the end of the freshman year can be predicted from the entrance test score. At the end of the year when all the data are available, what would be the graph you would use to display the data?
A scatterplot with GPA on the y-axis and the entrance test scores on the x-axis.
Questions 13-14 are fill in the blank and based on the regression from Question 11. Ifa student studies for 0 hours, we would expect them to have a score of what?
A scoreof 20
The correlation here is
A)0.66 (note positive and moderately strong upward cloud of points)
The regression line that would be used for predicting the birthweight would be
A)y = -932.4 + 70.3x Note positive slope (which goes with positive correlation). Negative intercept is where the line crosses the y-axis when x = 0 (and a value of 1932 is clearly excluded by the graph)
. Which of the following is not a measure of spread or variability in a data set?
All of the above measure the spread or variability.
Which of the following is an advantage of randomizing in experiments.
All of the above.
Which of the following is necessary to conduct a study properly?
All of the above.
The Division of Traffic and Parking at a large university wants to know the percentageof students who used the campus bus system on homecoming. They take a randomsample of four hundred students and find that 20% of them have used the bus systemduring the past week.4 points eachIn this study what are the: population sample parameter statistic margin of error
All students at this large university. The 400 students chosen. The percentage of all students that used the bus on homecoming. 20% 0.05
Suppose you are conducting an experiment that involves assigning each of 100 partic-ipants to one of two groups: Group A or Group B. Which of the following would notbe considered to be a random assignment of participants to groups?
As the participants show up for the study, assign the first 50 of them to GroupA, and the last 50 to Group B.
Whichis true about Histograms A and B below?
B. They both have a similar median but the mean for histogram B would be larger.
Use the following information for questions 11-14 two questions: Suppose an algebraprofessor found that the correlation between study time (in hours) and exam score(out of 100) is +.80, and the regression line was found to beScore= 20 + 4·Hours.He arrived at this equation through years of collecting data on his students, most ofwhom reported studying anywhere from 0 to 20 hours for his exams. For which valuesof study time does the professor's regression equation make sense in terms of predictingexam scores?
Between 0 and 20 hours.
Using the same information as the previous question, Using the Empirical Rule, 68%of adult males should fall into what height range?
Between 67 and 73 inches tall.
The shipping manager for this company has decided that they would like to pull aside the lightest 10% of these bags for repackaging. 10% of these bags are below what weight in pounds?
Between 7.4 and 7.55
A citrus fruit company ships bags of oranges throughout the country. The weight of these bags of oranges averaged 8 pounds with a standard deviation of 0.4 pounds. Also, a histogram of these weights followed the Normal distribution quite closely. What percentage of bags weigh less than 8.7 pounds?
Between 95 and 97
Pick which twoof the above would be wrong. Explain briefly.
C. is wrong since obesity is the response. E is wrong. Regardless of whether cortisol changes with the seasons or not -there is no reason to think that would affect the difference between obese and non-obese people(Since in that case both groups would have the same seasonal effect).
Researchers find a strong significant positive correlation in Minneapolis, Minnesota between weekly sales of hot chocolate and weekly cases of the flu. Which of the following is the best explanation?
C.There is a third variable like time of the year that is separately makingit more likely that people want hot chocolate and that more people get the flu.(note more flu and more hot chocolate sales in the winter with colder weather)
Randomly assigning subjects to groups in an experiment will help to
D.All of the above
The regression method isusually inappropriate
D.in all of the above circumstances.
The study of right-left grip strength differential is a matched pairs design because
For each unit we take two measurements and observe the difference
. Suppose the professor later found out that his correlation was not +0.80, but ratherit was +0.08. How does this change the predictions he can make about exam scoresbased on study time?
It won't change the predictions because the regression line stays the same.
The weight of the amount of meatsold at the butcher to individual customers atthat same market also averages 16 ounces but has a standard devation of 10ounces. Can you use the normal curve to find what percent of meatsales are for over 16.2 ounces? If so,find the percent. If not, explain why not.
It would not be legit to use the normal curve here. We know that none of the weightscan be negative but you get negative numbers as soon as you go 1.6 standard deviations below the mean, which is impossible for a normal curve. Clearly the weights would be very skewed to the right.
LABS & QUIZZES
LABS & QUIZZES
MIDTERM 2
MIDTERM 2
Suppose you look at two boxplots comparing weights of male cats versus female cats,and you find that the box for the males is much wider than the box for the females.What does this mean about the data sets?
Male cats have more variability in their weights than female cats.
OnApril 14, 1912, four days after it set sail from the port of Southampton England, the Titanic struck an iceberg in the North Atlantic. The ship sank and 1490 of the 2201 passengers perished. The table below shows a count of the survivors and victims of the Titanic sinking amongst third class passengers and the crew (first class and second class passengers fared much better but are not included in the table to ease the calculations for this problem). What is the proportion of the crew that survived? What proportion of the third class passengers survived?
Proportion of crew that survived = (192+20)/(862+23) ≈ 24%Proportion from third class that survived = (88+90)/(510+196) ≈ 25%
The probability that a fair die lands on 1 is 0.167, this means that if we roll the fair die many times we would expect it to land on 1 about 16.7 percent of the time. This is an example of...
Relative Frequency Interpretation
What was the relative risk of dying for a male crew member compared to a female crew member?What was the odds ratio for a male crew member compared to a female crew member?
Risk for male crew = 670/862 Risk for female crew = 3/23So relative risk = 670/862 divided by 3/23 = 0.777/0.130 = 5.96Odds for male crew = 670/192 odds for female crew = 3/20So odds ratio = 670/192 divided by 3/20 = 3.49/0.15 = 23.26
Would this data be considered to be skewed left, skewed right, or symmetric? Explain how you know. Does this make your answer to part a invalid? Explain why or why not.
Skewed left - mean smaller than median and long left tail (since min is much farther from Q1 than max is from Q3).Answer to part a is still valid.
Suppose that in a five-number summary you find that a larger gap exists betweenthe third quartile and the highest value than between the lowest value and the firstquartile. What does this mean about the shape of the data set?
Skewed right
We randomly select 1000 adults from a population of 2 million and also randomly select 1000 adults from a population of 20 million. Both samples ask the same question using the same methods. If the sample proportions are also the same, how will the margins of error compare for 95% confidence intervals for the true population proportion?
The MOE won't change with the larger population
Which of these are independent?
The amount spent on bread by two randomly selected customers at Trader Joe's Market in State College
A scale by the deli counter of a supermarket is used to weigh meats and cheeses and price the items purchased by customers. The scale is well calibrated, very reliable, and gives an unbiased measured weight. However, when the food is weighed it is inside of a plastic bag so the weights used to charge customers include the weight of the bag. The weights used to charge customers are then
The average customer at a convenience store spends $14. You are going to keep track of how much is spent by the customers. Which of the following is most likely to occur? Group of answer choicesA.a biased measurement of the weight of the food.(they would be systematically high)
The highest paid employee is randomly selected from the list of Fortune 500 companies. Which of these probabilities is the largest?
The chance this person is a college graduate.
Which of the following is a correct interpretation of a correlation?
The correlation is -0.85. This means that as the distance of a golf putt goes up,the success rate of making the putt goes down.
The Reeses Pieces applet we used recently in lab allowed usto randomly select a number, n, of Reeses Pieces and examine the distribution of the proportion of the sample that are orange when the population has a proportion, p, that are orange.Which of the following sampling distributions would not be appropriate to study with simulations from this applet.
The distribution of the average height of 50 adults chosen from a city with 300,000 adults whose average height is 67 inches with a standard deviation of 4 inches
If a student studies for one extra hour how much would we expect their score toincrease
The slope of the equation tells you that the score should improve by 4 pointsfor each additional hour studied.
We are going to randomly select 90 students from this university. What is the probability that the average number of credit hours taken by these students would be over 15 hours? Show your calculations.
The standard deviation of the mean = .221 z = (15 - 14)/0.221 = 4.52 which is off the charts for the normal curve so the chances are extremely small for the average being over 15.
Four of these trucks are selected at random.What's the chance that the average weight of those four trucks ismore than 74,000 pounds?
The standard deviation of the mean is 2500 now z = (74000 - 7000)/2500 = 1.6 which is between the 94thand 95th percentile so the answer is between 4% and 5%.
20% of the population of Pennsylvania are minors under 18 years old. a) (10 points) What is the probability that a random sample of 100 Pennsylvanians includes at most25 (25%) minors?
The standard deviation of the sample proportion is .04 So z = (0.25 -0.20)/0.04 = 1.25Which is at about the 89th percentile (so the answer is 89%)
Suppose the mean height for adult males in the U.S. is about 70 inches and the stan-dard deviation is about 3 inches. Assume men's heights are approximately normallydistributed. Using theEmpirical Rule, 95% of adult males should fall into whatheight range?
They should be between 64 and 76 inches tall.
A 2017 studey by researchers at University College London was publshed in the journal Obesity. They looked at2500 adults aged 54 and older. For each subject, asample of their hair was takenand the amount of cortisol in the hair was measured. Cortisol is a hormone that is released by the body in response to stress and low blood-glucose levels. It turned out that the level of cortisol was much higher in the obese subjects in the study. The authors speculated that stress might be a causal factor in developing obesity as it will increase cortisol levels.Keep in mind thathair is only a month or two old while obesity takes decades to evolve.a) (6 points) Is this research an observational study or an experiment? Explain briefly.
This is an observational study. The researcher does not assign people tobe obese or not or to specific amounts of Cortisol -they only observe (measure) how much cortisol is there and whether the person is obese or not.
What percentage of the loaves weigh between 15.5 and 16.5 ounces? Explain briefly.
This is asking about being within two standard deviations of the mean so the empirical rule says that about 95%would be in that interval.
A student takes a random sample of 1000 cars registered in Pennsylvania and checks the percentage of those cars that have had their emissions inspection completed. He found that 85% of the cars in his sample had the emissions inspection, so he calculated a 95% confidence interval for the proportion in the population to be 0.85 ± 0.023.
This says that student can be 95% confident that the true population proportion of cars that had their emission inspection is between 82.7% and 87.3%
If a Wawa location has monthly revenues in the top 3% of all Wawas in PA thenit receives an award from the corporate office. What would monthly revenue needto be to receive an award?
Top 3% would be the 97th percentile, from table a z-score of 1.88 is the 97th percentile, solving forgives a value of 2.55, so you need 2.55 million in revenue to be in-the top 3%.
Thirty-six of the mortgages are selected at random. What is the chance that more than 54% of those are for at least $2150? Hint: This should be set up as a question about sample proportions, i.e., what is the chance that the sample proportion is larger than 0.54. You should have p=0.5, from the first part, and n=36.
Using p=.5 and n= 36, we simply repeat the procedure of 4 and 9. Find the standarddeviation of the sample proportion, find the z-score, use the table.
One hundred different statistics students each take a random sample of 1000 cars registered in Pennsylvania and check the percentage of those cars that have had their emissions inspection completed. Each student used their data to make 95% confidence intervals for the proportion of all registered cars that have their emissions inspection completed. In this situation:
We would expect around 95 of the students to get the true proportion for Pennsylvania in their intervals.
A recent Gallup Survey taken between April 3rdand 6th, 2014 asked working American adults how long they could go without a job before experiencing significant financial hardship. Itturned out that 43% of the 509 people interviewed said they could go no more than a month. Gallup also reported that for these results, one can say with 95% confidence that the margin of sampling error is ± 5%. For this report what isThe population of interest? The parameter of interest The sample? The statistic?
Working American adults % of Working American adults who could go without a job no more than a month with significant hardship(alternative answer: average amount of time working American adults can go without a job before experiencing significant hardship) The 509 adults interviewed 43%
45% of the babies born at a large hospital are girls. Which is more likely?
a majority of the next 20 babies are girls
Regular Gallup Poll interviews taken daily for an entire year examined the issue of the difference in the health of American adults aged 18 to 64 who have health insurance versus those who do not (they were not interested in those 65 and older since they would all be eligible for health care through the Medicare program). Altogether, 199,672 respondents were interviewed as part of this investigation including about 160,000 who had health insurance and 40,000 who did not. It turned out that 57% of those with health insurance rated their own health as "excellent" or "very good" compared withonly 36% of those without health insurance. For results based onthe sample of those 40,000 with no health insurance, the Gallup report indicated that the margin of error was ± 1 percentage point.a.(15points)For this report what is The population ofinterest? An example of a parameter of interest? The sample? An example of a statistic? The sample size?
american adults aged 18 to 64 % of american adults aged 18 to 64 who rate their health as excellent or very good 199,672 57% for insured group or 36% for uninsured group the 199,672 respondents
A recent publication examined whether the presence of your cell phone causes changes in your ability to concentrate. In this study, 520 subjects were randomly assigned to either leave their cellphones in another room, have their cell phones with them but out of site in their pockets or bags, or have their cell phones visible on a desk in frontof them. It turned out that the subjects who left their cell phones in a separate room scored 10% better on a memory task compared to subjects whose phone were in their pockets or bags and 12% better than those whose phone was on the desk in front of them. THIS IS AN EXAMPLE OF IN THIS SITUATION
an experiment that is not double blind The location of the cell phone is the explanatory variable and the score on the memory task is the response.
Some critics of the poll said that the results regarding the health differences between those who were insured and those who were not may be due to the other factors besides their access to medical care. For example, 36% of the people without health insurance are smokers compared with only 20% of the people with health insurance. These critics
are pointing to a confounding factor in interpreting the results.
Which is more likely?
between 500 and 700 of the next 1000 fill their tanks
60% of the customers at a gas station fill up their tanks. Which is more likely?
between 58% and 62% of the next 1000 customers fill their tanks.
One store sells these oranges for $0.50 per pound. What percent of the bags sell for less than $4.35?
between 95 and 97
Compare the three boxplots below: Which of the three distributions is skewed to the right? Which of the three distributions has the least variability? Which ofthe three distributions has the largest 75thpercentile?
c A B
Which is more likely?
exactly 60 of the next 100 fill their tanks.
A measurement will have less bias if it is more reliable
false
If regression is appropriate for prediction, then it is also appropriate for making causal statements.
false
If the correlation between two variables is zero then they are unrelated.On April 14, 1912, four days after it set sail from the port of Southampton England, the Titanic struck an iceberg in the North Atlantic. The ship sank and 1490 of the 2201 passengers perished. The table below shows a count of the survivors and victims of the Titanic sinking amongst third class passengers and the crew (first class and second class passengers fared much better but are not included in the table to ease the calculations for this problem).
false
In reporting the results of a poll, the margin of error will be larger if the population size is higher.(Note that the MOE would be larger with a smaller smple size
false
The correlation between mileage and engine displacement is positive.
false
The correlation between the price of the dinner and the tips left by customers at a restaurant is 0.96. True or False:If every customer decided to give one dollar morein tips then this correlation would go up.
false
The events that a customer pays with a credit card and the event that a customer pays with an American Express card are mutually exclusive. Recall that two events are mutually exclusive if they have no outcomes in common, or if one event happens, then the other does not.
false
The purpose of a placebo is to reduce the variability of experimental data.
false
True or False: The margin of error is larger for an 80% confidence interval than for a 90% confidence interval?
false
True or False: The monthly mortgage payments follow the normal curve.
false
Suppose that the monthly revenue of all Wawas in Pennsylvania has a mean of 1.8million and a standard deviation of 0.4 million. The histogram of revenues appears tobe approximately bell-shaped and symmetric. What percentage of Wawas have monthly revenues of over 1 million dollars?
from table z=-2 is the 2nd percentile, so 98% of Wawas have revenues over 1million.
One of these skeletons (identified by the X)had a metacarpal size of 52 mm and a height of 183 cm. If the height of this skeleton had been misrecorded as 153 cm, then the correlation between stature and metacarpal length for these 10 skeletons (including the misrecorded value) would
go down
f instead the question in part a had asked about the probability that a random sample of 100 Pennsylvanians included between 15% and 25% minors(inclusive); would the answer be smaller, larger, or stay the same? Explain how you know.
it would be smaller because this event is just a subset of being at most 25%
The report gives results for all 199,672 18-64 year old adults interviewed as well as separately for the insured and non-insured groups who responded. If Gallup had reported the margin of error for the sample percentage of all adult respondents who said their own health was excellent or very good it would be
less than 1%.
A new metacarpal bone, which is45 mm long, is found at an archeological dig. An investigator wants to use the data from the 10 skeletons mentioned above to make a prediction about the height of the person this new metacarpal bone came from. For the new metacarpal bone that was found,you would expect it to come from a skeleton that was ______________cm tall. Fill in the blank and show your work.
linear relationship and 45 is within the range of the data so it is legit to use the linear regression to estimate estimated height of skeleton = 170.82
80% of the students in a statistics class do not smoke while some smoke every day. The students write down the number of cigararettes they smoked yesterday. This says that the:
median number of cigarettes smoked is smaller than the standard deviation of those numbers.
Ninety-eight percent (98%) of households in Pennsylvania have a refrigerator in their home. Would it be appropriate to use the Normal Approximation to calculate the chance that less than 95% of a random sample of 100 Pennsylvania households have a refrigerator.
no
Suppose 100 passengers are randomly selected. What is the probability that at least 70% of them would not receive a meal under this plan?
p=.65 is the proportion who would not get a meal and n= 100 is the sample size.We repeat the same z-score and standard deviation calculations as in 4 and 9 to get the answer.
What is the parameter that the sample statistic (43%) is estimating?
percentage of Cincinnati voters who favor a half-percent increase in the sales tax to fund mass transit
The airline is thinking of eliminating the meal service for all passengers except those in business or first class. What is the probability that a randomly selected passenger would not receive a meal under this plan?
probability of receiving a meal = .3 + .05 = .35 1-.35= .65 There is a 65% chance that a randomly selected passenger would not receive a meal under this plan.
A study sought to learn if patients getting hip replacements had experienced more falls in the past year than patients at the same medical practice who were having knee surgery. This would be a
retrospective observational study.
The term __________ refers to the idea that sample statistics will differ from sample to sample and not necessarily be equal to the population parameter.
sampling variability
Find a 90% confidence interval for the parameter. (Be sure to indicate what you find for the standard error of the statistic, the multiplier number (z*), and the final confidence interval -
standard error= .017 multiplier= 1.64 CI=0.43+/- 1.64 x 0.017
Suppose that Gallup had conducted a similar survey of 509 workingadults, using the same methodology, but only in CentreCountyPennsylvaniato estimate the percentage of CentreCounty working adults who could last no more than a month before suffering significant financial hardship. The margin of error for that survey would then be
still about 5% Since the sample size is the same, the MOE would not change. Population size does not affect the MOE as long as the sample is a small part of the total as in these cases
•Suppose that 30% of Penn State students are from Philadelphia county. We are going to simulate taking repeated samples of size n=100 from the Penn State student population, and computing the proportion of these samples that are from Phila county. This question is based on the stat key simulation activity: What is the shape of the sampling distribution's histogram?
symmetrical and bell-shaped
A report in The New England Medical Journal described a study of the effects of hormone therapy on middle-aged women. About 950 women took part in the study; half were selected randomly to receive the hormone therapy and the other half was given a placebo. After about a year, blood tests were conducted on each subject by a lab technician who was unaware of which group (treatment or placebo) the blood samples originated from. In presenting the results of the experiment, the authors reported that the women in the treatment group had experienced a significant increase in HDL (the so-called "good" cholesterol) and a significant decrease in LDL (the so-called "bad" cholesterol) when compared with the control group. A newspaper report said the experiment had shown that hormone therapy is effective in reducing the women's risk of heart attack. This may not be a justified conclusion because:
the cholesterol measurements may not be a valid measure of the risk of heart attack.
A research team compared two methods of measuring tread wear on tires. Eleven tireswere each measured for tread wear by two different methods: one method was basedon weight while the other method was based on groove wear. For convenience, eachtire was measured first by weight method and then second by the groove wear. Whatis the experimental or observational unit?
the tires
Overall, the risk of dying was higher for the crew than for third class passengers. However, the opposite was true amongst the men and amongst the women separately (i.e. the crew had a lower risk for each gender). This is because
there were very few women amongst the crew and so breaking things down by gender created a Simpson's Paradox.
In a study of the effect of leisure exercise on diabetes, researchers followed 44,828 Chinese adults who were diagnosed in 1996 with impaired fasting glucose (an indicator of being at high risk to develop Type II Diabetes) and then followed them for 18 years until 2014. The lifestyles of these people wereclassified as to being inactive or having a low, moderate or high amount of phsyical activity in their leisure time. Compared to the subjects in the inactive group, the percentage of people who developed Diatbetes during that 18 year period was reduced by 12% (low activity), 20% (moderate activity), and 25% (high activity). Since the study's purpose was to examine leisure time activity, these results were adjusted for the amount of physical labor the subjects did at work.The reason why the researchers adjusted for the amout of physical labor at work was
to try and remove labor at work as a possible confounding factor.
A matched pairs design helps to lower the variation in the response variable.
true
A parameter is a number that describes the population.
true
A placebo helps avoid bias that might result when the subject knows what treatmenttheyare getting.
true
A poor question wording can cause bias even in a complete census.
true
A random sample can't eliminate the bias caused by a poor question wording.
true
If the regression line has a negative slope then the correlation will also be negative.
true
If the sample size is quadrupled than the standard deviation of the sample mean will be cut in half.
true
If two events are mutually exclusive, then the probability that one or the other of the two events happening is the sum of their individual probabilities
true
If two events are mutually exclusive, then the probability that one or the other of the two events happening is the sum of their individual probabilities.
true
If we give a $50 holiday bonus to every waiter at a restaurant then the standard deviation of their wages will not change.
true
In spinning a roulette wheel, there is a 47% chance that the result comes up red. True or False:Thus, the chance that red comes up a majority of the time is greater with 50 spins than it is with 700 spins.
true
In tossing a regular six sided die, the chance that the average of your rolls comes out between 3 and 4 is higher when you have 1000 rollsthan when youhave 50 rolls.
true
Since 48% of babies are girls, you are more likely to get a majority of girls in the next 50 babies than you are in the next 200 babies.
true
Suppose that 68% of Penn State students were born in PA. I am interested in taking random samples of 36 students, and calculating the proportion of the sample that is was born in PA. True or false: The distribution of the proportion of students in the sample that were born in PA is normal with a mean of 0.68
true
The amount of gas purchased by customers at a gas station averages 12 gallons with a standard deviation of 5 gallons. Suppose I am interested in the average amount of gas purchased by the next 100 customers. True or false: the distribution of the average amount of gas purchased by the next 100 customers is normal with a mean of 12 galloons.
true
The difference in the proportion of smokers with visible wrinkles and non-smokers with visible wrinkles is statistically significant.
true
The expected value of a measurement is the long run average value of the measurement when you repeat the measuring process over-and-over again. It does not have to be an actual possible value for the measurement.
true
There is about an 8% chance that a coin lands heads exactly 50 times out of 100 tosses. True or False:From that information, we can see that the chance of getting exactly 500 heads out of 1000 tosses is less than 8%.
true
Thirty percent of the math majors at one university are women. A math major is selected at random. True or False:It is impossible to have a 35% chance that the selected student is a women with a minor in finance.
true
f the standard score isnegative than the value must be below the mean.
true
the average of a list of numbers is negative,then the average will be smaller than the standard deviation.(Note that negative numbers are smaller than positive ones)
true
What percent of the loaves weigh over 16.2 ounces? Show your work/Explain
we have z = (16.2 -16)/0.25 = 0.8from the tables we see that 0.8 is at about the 79thpercentile so about 21%lies above that.
Correlations will give a deceiving impression of the strength of an association
when the pattern of points in the scatterplot is not linear.
In the German GPA example, would a student with a GPA of 90.5 be graduating with distinction?
yes
The GPAs of Stat 100 students average 3.0 with a st. dev. of 0.5 and follow the normal curve pretty closely. Would it be appropriate to use the Normal Approximation to calculate the chance that 2 randomly selected students have an average GPA between 2.85 and 3.15?
yes
rucks loaded with corn arriving at a granary weigh an average of 70,000 pounds with a standard deviation of 5,000 pounds and a histogram of these weights approximately follows the normal curve. What percentage of these trucks weigh more than 74,000 pounds?
z = (74000 - 70000)/5000 = 0.8 which is around the 79thpercentile so the answer is 21%
What percentage of Wawas have monthly revenues under 2 million dollars?
z=0.5 is the 69th percentile, so 69% have revenues under 2 million.