STAT 2331 Final Exam
A pollster took a random sample of 100 students from a large university and computed a confidence interval to estimate the percentage of students who were planning to vote in the upcoming election. The pollster that the confidence interval was too wide to provide a precise estimate of the population parameter. What could the pollster have done to produce a narrower confidence interval?
Increase the sample size to 200
In the National Hockey League a good predictor of the win percentage of games won by a team is the number of goals the team allows during the season. Data were gathered for all 30 teams in the NHL and the scatterplot of their Winning Percentage against the number of Goals Allowed in the 2019/2020 season with a fitted least-squares regression line is provided: Winning Percentage=116.95-0.26*Goals Allowed R^2=0.69 Which of the following is the best interpretation of the y-intercept?
Interpreting the y-intercept in this context would involve extrapolation and is best avoided
Which of the following statements about the One Sample t Test is NOT true ?
Is has lower probability of making a Type 1 error than the Sign Test
Which of the following properties is NOT a property of correlation , R ?
It ensured the strength of any type of relationship between x and y
Which of the following properties is NOT a property of correlation, R?
It measures the strength of any type of relationship between x and y.
A study looked at the relationship between televisions and physicians. For 32 countries, the researchers recorded the number of people per TV set in that country and the number of people per doctor in that country. The found a correlation of R=0.852. After the study was completed, the researchers realized that people in wealthier countries tend to have more TVs and better access to healthcare. What type of variables is wealth of a country?
Lurking
An educator is interested in determining the number of hours of TV watched by 4 - year - old children . She wants to test the claim that the average number of hours watched per day is less than 4 hours . She plans to take a SRS of 100 youngsters to test her claim . If the true mean number of hours watched per day is 3.8 , then the power of her test is 0.80 . This means that in all possible samples of size 100 she will
Make a Type II error 20% of the time
A recent poll indicates that 48% of all registered voters in America plan to vote for a specific candidate in the upcoming presidential election. Suppose a random sample of 20 Americans is taken. Let X represent the sample count who plan to vote for the candidate. What is the mean and standard deviation of X?
ux= 20(0.48) ox= square root 20(0.48)(0.52)
The purpose of a confidence interval for u is
To give a range of reasonable values for the population mean
The following data is from a SRS taken of adult Americans. It was used for a study by the National Opinion Research Center to determine if there was an association between gender and number of hours of home religious activity. What other graphical or numerical summary would be appropriate for this data?
stacked bar chart
An experiment comparing three drug types--A, B, and C--is performed. A group of subjects is divided into three groups by age: 20-40, 41-60, and 61+. The 20-40 year olds receive drug A, the 41-60 year olds receive drug B, and the 61+ receive drug C. People administering the drug know which subject is receiving which drug, but the subjects do not. Time to relief is measured for each subject. There are obvious confounding variables in this experiment. They are:
the age of the subjects and the drug types
The accuracy of the Normal approximation to the binomial improves when:
the number of observations, n, increases
A Q-Q plot that demonstrates a linear pattern allows one to assume:
the sample data set was drawn from a population that is normally distributed
Two variables are confounded if:
their effects on the response variable cannot be distinguished
A dietician conducted a study to determine if the diet of college students depends on whether the student has a family history of diabetes. A SRS of 50 students with a family history of diabetes and 50 students without a family history of diabetes was taken. The dietician then recorded whether or not each student had a healthy diet. Test the claim that the proportion of students with a family history of diabetes who have a healthy diet is greater than the proportion of students without a family history of diabetes who have a healthy diet. Conduct a 99% confidence interval for pyes-pN0.
(-0.0098, 0.4898)
A National AIDS Behavioral Survey randomly sampled 1000 adult heterosexuals and gave each a survey regarding their sexual practices. The study found that 64 of the participants had multiple partners. Construct a 98% confidence interval for the proportion of adult heterosexuals with multiple partners.
(0.046, 0.082)
An actuary is interested in estimating the proportion of young adults who plan to have children someday . She takes a SRS of 60 young adults and finds that 48 of them plan to have children . Construct a 90 % confidence interval for the proportion of young adults who plan to have children someday .
(0.715, 0.885)
In a SRS of 25 men, the mean systolic blood pressure is 123.5 and the standard deviation is 9. Construct a 90% confidence interval for the mean systolic blood pressure of men.
(120.420, 126.580)
Let X represent a continuous random variable with a uniform distribution over an interval from 0 to 4. What is P ( X = 1.75 ) ?
0.0000
A psychologist takes a SRS of 100 SMU students to test the claim that the proportion of students who are unhappy with their weight is greater than 0.5. She sets α=0.01. In her sample, 67 students say they are unhappy with their weight. What is the p-value for this test?
0.0003
Suppose it is known that 10% of adolescent females in the United States have iron deficiency. Suppose a random sample of 150 adolescent females were taken; use the normal approximation to the binomial to find the probability that less than 3 have iron deficiency.
0.0005
A cookie company has decided to sell its cookies in packages that are advertised to contain "less than 100 calories." In truth, the calorie count per package is normally distributed with mean 95 and standard deviation 4. What is the probability that a randomly selected package of cookies will have a calorie count more than 105?
0.0062
Some argue that millions of Americans are so hooked on television that their viewing habits fit the criteria for substance abuse as defined in the official psychiatric manual. Young people (aged 19 to 25) were selected at random and asked, "In the past seven days, how many days did you watch television?" A probability model for the response, X, is given below. What is P(X≤ 2)?
0.13
Spell-checking software catches "non-word errors" such as when "the" is typed "teh". When undergraduates were asked to write a 250-word essay (without spell-checking), the number X of non-word errors has the following distribution: What is P(X≥3)?
0.4
Let X represent a continuous random variable with a uniform distribution over the interval from 0 to 3. What is P(X>0.9)?
0.7
If X~N (15, 5), what is the P(X>11)?
0.7881
If X~N (15,5), what is the P(X>11)?
0.7881
Suppose that 77% of the students at a small private university carry student loans. For a SRS of students at this university, let p hat be the sample proportion of students who carry student loans. In a sample of n=100, what is the probability of choosing a SRS in which more than 70% of the students carry student loans?
0.9519
The life spans of a species of fruit fly are normally distributed with a mean of 36 days and a standard deviation of 4 days. A SRS of 16 fruits flies is taken. What is the probability that the sample mean life span is between 34 and 38 days?
0.9545
Which of the following statements about the t distribution is / are true ? 1. The t distribution is used in confidence intervals for a population mean when is estimated with s. 2. As the sample size increases , the t distribution gets closer to a standard normal distribution 3. There t distribution is the same regardless of the sample size .
1 and 2 only
Which of the following are true of p hat? 1. p hat is a statistic 2. p hat is a categorical random variable 3. p hat describes categorical data
1 and 3 only
You must choose 4 numbers from the integers 1 to 10, with repeats NOT allowed. Choose four numbers that have the largest possible standard deviation.
1, 2, 9, 10
Which of the following are true of p hat? 1. p hat is a statistic 2. p hat is a quantitative random variable 3. p hat describes categorical data
1, 2, and 3
The following data is from a SRS taken of adult Americans. It was used for a study by the National Opinion Research Center to determine if there was an association between gender and number of hours of home religious activity. What is P(A u C)?
1042/1400
A university held a blood pressure screening clinic for its professors . The results are summarized in the table below by age group and blood pressure level. What is the probably a randomly selected professor has high blood pressure?
124/219
Suppose a researcher is interested in determining the average length of gestation among pregnant Canadian women. Gestation length is approximately Normally distributed. He takes a SRS of 36 Canadian women who have given birth within the last year and calculates the length of gestation in days for each of them, getting a sample mean of 272.25 and a standard deviation of 14.25. How many pregnant Canadian women should be sampled in order to get a 95% confidence interval with a width of 4.8?
142
Suppose you want to estimate the proportion of employed adults who would continue working if they won 10 million dollars in the lotteryA previous study on the issue had a sample proportion of 0.59. How many employed adults should be randomly sampled in order to get a 99% confidence interval with a width of 0.2?
161
Which of the following statements about the t distribution is/are true? 1. The t distribution is used in confidence intervals for a population mean when o (standard deviation) is known. 2. As the sample size increases, the t distribution gets closer to a standard normal distribution. 3. There is a different t distribution for every different sample size.
2 and 3 only
The following data is from a SRS taken of adult Americans. It was used for a study by the National Opinion Research Center to determine if there was an association between gender and number of hours of home religious activity. What is P(A∩C)?
229/1400
The following data is from a SRS taken of adult Americans . It was used for a study by the National Opinion Research Center to determine if there was an association between gender and number of hours of home religious activity. What is P(A|C)?
229/505
A recent study demonstrated that 25% of American women are red/green color blind. Which of the following is more likely?
250 out of the next 1000 women will be color blind.
A test of H0: u=25 and Ha: u≠25 is going to be conducted based on a SRS of size 30. Which of the following test statistics will have the smallest p-value associated with it?
3.4
A survey involving 35 questions was given to a sample of 200 students attending a university with an enrollment of 10,000. How many variables does the data contain?
35
A test of H0 (null hypothesis) : p=0.4 versus H a (alternative hypothesis) : p>0.4 is going to be conducted based on a SRS of size 50. Which of the following test statistics will have the smallest p-value associated with it?
4.1
The amygdala is a brain structure involved in the processing and memory of emotional reactions . In a research project , 10 subjects were shown emotional video clips . Then they had their brains scanned with positron emission tomography ( PET ) , and their memory of the clips was assessed quantitatively . The scatterplot below displays the results for the relative amygdala activity and the memory score for each subject . The R^2 value for this study was 0.4582. Interpret what this means.
45.82% of the variation in memory score is explained by the regression on relative amygdala activity.
Let X be the resting heart rate of a physically fit man . Assume that the resting heart rate for fit men follows a Normal distribution with mean 60 and standard deviation 10. Let be the sample mean resting heart rate for a randomly chosen sample of 35 fit men . What value is the 95th percentile of all sample mean resting heart rates?
62.78
A university held a blood pressure screening clinic for its professors. The results are summarized in the table by age group and blood pressure levels. What is the probability a randomly selected professor who is 50 or over has high blood pressure?
73/104
A sociologist is planning to test the claim that the proportion of Americans who believe in heaven is more than 0.75 at the α=0.05 significance level. If in reality the true proportion of Americans who believe in heaven is 0.78 and he plans to take a SRS of 100 Americans, the the power of the test is 0.85. In all possible samples of size 100, what percent of the firms would he fail to reject the null hypothesis?
75%
The following data is from a taken of adult Americans. It was used for a study by the National Opinion Research Center to determine if there was an association between gender and number of hours of home religious activity. What would the value of P(A|C) have to be in order for A and C to be independent events?
766/1400
Each of the 110 students in a statistics class selects a different random sample of 35 quiz scores from a population of 5000 scores they are given. Using their data, each student constructs a 90% confidence interval for u, the average quiz score of the 5000 students. Which of the following conclusions is correct?
About 90% of the confidence intervals will contain u
A real estate agent in Texas is interested in answering the question "What is the average price of a home in the United States?" She takes a SRS of 100 homes from a list of the selling prices of all of the homes sold in Texas by her company in the past month. The graphs and charts calculated from the data are shown below. What is the sample frame?
All homes sold in Texas by the agent's company in the past month
An Internet survey asks women if they have ever had an abortion. Which type of bias might affect the responses to this kind of question?
All of the other answers are correct
An instructor is going to model an experiment in his statistics class by comparing the effect of 4 different instructional methods on student responses. There are 40 students in the class. Which is the best way for the instructor to randomly assign the students to the 4 treatments for this experiment?
Assign a unique number to each student, then use random numbers to assign 10 students to the first treatment, 10 students to the second treatment, and so on.
Suppose X~N ( 23 , 4). Between which two numbers would the middle 92 % of all X values fall ?
Between 16 and 30
There are two data sets taking the following values. Data Set A: 0 1 2 3 4 5 6 7 8 9 10 Data Set B: 0 1 2 3 4 5 6 7 8 9 50 Which of the following is true? You do not need to do any calculations to answer this problem.
Both the mean and standard deviation are larger in Data Set B
A social scientist is interested in alcohol abuse among college students. She samples 100 students from SMU and another 100 students from TCU and asks each one, "On how many days in the past week did you consume at least one alcoholic drink?" She is especially interested in the proportion from each university who had an alcoholic drink on 5 or more days. Which of the following inference methods is appropriate for this situation?
Confidence Interval for a Difference in Proportions
The side-by-side boxplots below come from three different data sets, all with 30 observations in both groups. Which data set has the most evidence of association between the explanatory and response variables, and which has the weakest evidence of an association between the explanatory and response variables?
Data Set C had the strongest evidence of an association; Data Set B has the weakest evidence of an association
The proportion of baby boys born in the United States is equal to 0.512. The two histograms below represent repeated samples of newborn babies in the United States. What is the best explanation the difference in the spread of the distributions?
Different sample sizes are being used
Bone strength of dominant and non-dominant arms were collected for 15 baseball players. Suppose we want to predict the strength of the dominant arm Y using only the strength of the non-dominant arm X. The least squares regression line is y hat=1.373x+0.866. What is the correct interpretation of the slope of this line?
For every increase of 1 in strength of the non-dominant arm, the strength of the dominant arm increases by 1.373.
Research has confirmed that listening to music can have significant positive impact on perception of chronic pain. US researchers tested the effect of music on 60 patients who had endured years of chronic pain. Half of the 60 patients were randomly assigned to listen to music on a headset for an hour every day for a week, while the rest did not. Of those who listened to music, 23% reported a drop in pain level. Of who did not listen to music, 5% reported a drop in pain level. What can be concluded from this study?
For people with chronic pain, listening to music might cause them to experience a drop in pain level, but we cannot know for sure since this study will suffer from the placebo effect.
Recently a study was conducted to determine whether females are more likely to smoke than males. An SRS of 100 females and another SRS of 100 males were taken and asked whether or not they were smokers. Test the claim that the proportion of females that smoke is greater than the proportion of males that smoke. What is the correct hypotheses to test the claim? Let p1= the proportion of females that smoke p2= the proportion of males that smoke p= the proportion of all people that smoke
H0: p1=p2 Ha: p1>p2
A psychologist takes a SRS of 100 SMU students to test the claim that the proportion of students who are unhappy with their weight is different from 0.5 . She sets a 0.01 . In her sample , 67 students say they are unhappy with their weight . What are the appropriate null and alternative hypotheses to test her claim ?
H0: p=0.5 Ha: p≠0.5
A researcher gathers data on how long it takes smokers to fall asleep . Which graphic would be the best choice for her data ?
Histogram
A real estate agent in Texas is interested in answering the question " What is the average price of a home in the United States ? " She takes a SRS of 100 homes from a list of the selling prices of all of the homes sold in Texas by her company in the past month . The graphs and charts calculated from the data are shown below. What is the population of interest?
Homes in the United States
Suppose I want to test whether the judges from a figure skating contestant's own country rate their contestant better than foreign judges . What's the best way to design an experiment to investigate this ?
Matched pairs design
Suppose a test of H0: u1-u2=0 and Ha: u1-u2 ≠0 is run with α=0.10 and a p-value =0.069. If you were to calculate a 90% confidence interval for u1-u2, would the resulting interval contain 0?
No, because based on the p-value for the hypothesis test would we reject the null, which implies that 0 is not a plausible value for u1-u2.
Suppose that in a church with 30 members, 55% support a candidate for public office. Suppose an SRS of 5 church members is selected and the total number of people who support the candidate is counted (out of the 5). Does this constitute a binomial experiment?
No, because p is not constant from trial to trial.
A tax assessor wants to test the claim that the mean property bill for all homeowners in Madison, Wisconsin, is greater than $1400. He takes a SRS of 40 homeowners and records the amount each pays in property taxes. The results of his study are below. Have the assumptions been satisfied to conduct a One Sample t Test for the population mean?
No, the data is highly skewed with outliers.
An admissions counselor at a private university wants to test the claim that the average high school GPA of students attending his school was greater than 3.60. He takes a SRS of 25 students and records the high school GPA for each one. His results are shown below. What can the counselor conclude at the α=0.01 level?
None of the above; the conditions for this test are not met
A real estate agent in Texas is interested in answering the question "What is the average home price of a home in the United States?" She takes a SRS of 100 homes from a list of the selling prices of all of the homes sold in Texas by her company in the past month. The graphs and charts calculated from the data are shown below. Which of the following is NOT a source of bias in her study?
Only 100 homes were in the study
Which of the following is true of p hat?
P hat is a quantitative random variable
The following data is from a SRS taken of adult Americans. It was used for a study by the National Opinion Research Center to determine if there was an association between gender and number of hours of home religious activity. What would the value of P(B|A) have to be in order for A and B to be independent events?
P(B)= 65/1400
The boxplots above summarize maximum temperatures of cities in Australia. Which city records the highest maximum temperature?
Perth
An individual requires a warm, stable climate. Based on the histograms below, which city is better for them?
San Diego; the mean temperature is higher and the standard deviation is lower
A statistic students favorite cereal states that the net contents of the box weigh 12 ounces. The student suspects the mean weight is less than the 12 ounces since the boxes never seem full. She takes a SRS of 20 bites and weighs the contents of each, finding a sample mean weight of 11.8 ounces and a sample standard deviation of 0.4 ounces. Based on the resulting p-value=0.0188, what conclusion would she makes at the α=0.01 significance level? Suppose she later learned the true mean weight is 11.9 ounces. Was her conclusion correct, or was it an error?
She would fail to reject the null, making a Type II error.
An instructor at a university believes that there is an association between a student's major and the number of hours he / she spends studying.per week . If she collects data to test this claim , which of the following would be most appropriate to describe her data set ?
Side-by-side boxplots
Suppose a test of H0: p1=p2 and Ha: p1≠p2 is run with α=0.05. The p-value of the test is 0.023. What should be concluded?
Since the p-value is less than α, there is sufficient evidence at the 0.05 level to conclude that the proportions are different.
Identify the numbers in this situation as either statistics or parameters; a fish hatchery released thousands of fish into local streams and rivers. 60% of the fish released were rainbow trout. A biologist returned two months later, took a sample of fish, and found their mean length to be 18.2 inches.
Statistic: 18.2 Parameter: 60%
Identify which number is the statistic and which is the parameter . Suppose the proportion of American voters who plan to vote for the Republican candidate is 51 % In an election poll that samples 700 American voters , 46 % say then plan to vote for the Republican candidate .
Statistic: 46% Parameter: 51%
Recently a study was conducted to determine whether females are more likely to smoke than males . An SRS of 100 females and another SRS of 100 males were taken and asked whether or not they were smokers . Test the claim that the proportion of females that smoke is greater than the proportion of males that smoke . What is the behest test statistic and p-value?
TS= -1.04 p-value= 0.8514
Suppose that 70% of Americans support the death penalty for persons convicted of murder. Let p hat be the sample proportion of people who support the death penalty in an SRS of Americans. What is the minimum sample size required for p hat to be appropriately Normally distributed?
The distribution of p hat will be approximately Normally distributed if the sample size is at least 34.
What can be concluded from the residual plot below regarding the relationship between two quantitative variables, X and Y?
The response is not normally distributed for each x value
A test is given to two classes (Class 1 and Class 2) and the scores are summarized as the histograms below. What can we conclude regarding the standard deviations for the two classes?
The standard deviation for Class 1 is larger than that for Class 2.
A test is given to two classes (Class 1 and Class 2) and the scores are summarized as the histograms below. What can we conclude regarding the standard deviations for the two classes?
The standard deviation for Class 2 is smaller than that for Class 2.
A professor wants to know if her students live less than 15 miles away from school, on average. She takes a SRS of 35 students from her class and records the distance that each one lives from campuses. What can the professor conclude at the α=0.05 level (Hint: You have to decide which of the two tests shown is appropriate).
There is enough evidence at age 0.05 level to conclude that the median distance from campus for students attending his university is less than 15 miles.
Studies that compare treatments for chronic medical conditions such as headaches can use the same subjects for each treatment. One such study considered a drug (a pill called Sumatriptan) for treating migraine headaches in children. The study observed each of 30 children at two times when the child had a migraine headache. They received the drug at one time and a placebo at the other time. The order of treatment was randomized and the study was double-blind. For each child, the response was whether the drug or the placebo provided better pain relief. Of the 30 children, 22 had more pain relief with the drug and 8 had more pain relief with the placebo. Let p denote the proportion of children having better pain relief with the drug, in the population of children who suffer periodically from migraine headaches. Suppose you want to test the claim that more than half of the population gets better pain relief with the drug. Assuming that the p-value is smaller than α=0.05, what should you conclude?
There is enough evidence that the true proportion of children who get better pain relief with the drug is greater than 0.5.
A psychologist takes a SRS of 100 SMU students to test the claim that the proportion of students who are unhappy with their weight is different from 0.5. In her sample, 60 students say that they are unhappy with their weight. What conclusion would she make at the α=0.01 level?
There is not enough evidence at the 0.01 level to conclude the proportion of students who are unhappy with their weight is different from 0.5.
A pharmaceutical company wants to test its claim that fewer than 20 % of patients who use a particular medication will experience side effects . They do a hypothesis test at the α= 0.05 significance level and calculate a p-value of 0.08 . If in reality 19 % of all patients on this drug experience side effects , which of the following is true ?
They will have failed to reject H0 and made a Type II error
Let x be the number of acres burned by a wildfire in the United States. Since some of the wildfires burn thousands of acres, the distribution of acres burned by wildfires is strongly right skewed with a mean of 780 acres and a standard deviation of 500 acres. Suppose a SRS of 15 wildfires is taken. Which sample mean would be larger than 85% of all other sample means for number of acres burned?
This is impossible to find because we do not know the distribution of the x bar
Hyla chrysoscells is a type of gray tree frog with a distinct mating call. Frogs are cold-blooded animals, and their physiology is affected by variations in temperature. Field biologists wanted to know if the mating call of H. chrysoscelis is affected by the temperature of its natural habitat. Here is a scatterplot and regression output of the note- repetition frequency (in notes per second) of the mating call for 20 chrysoscelis in the wild, as a function of habitat temperature in degrees Celsius). Assuming the conditions for least squares regression are met, what is the predicted mating call frequency for a temperature of 35 degrees Celcius?
This regression should not be used to make predictions for a temperature of 35 degrees Celsius
A city official wants to compare the proportion of City of Dallas residents and their suburban residents who frequent Klyde Warren Park. Which of the following inference methods is appropriate for this situation?
Two proportion Z Test
Getting an adequate amount of sleep can improve a variety of physiological functions, and it is known that the average number of hours that people sleep each night is Normally distributed. A psychiatrist at a major research center takes an SRS of 25 emotionally disturbed patients and records the average amount of sleep that each gets on a typical night. He summarizes the data and finds that x bar=6.90xˉ=6.90 and s=0.878s=0.878. Suppose a 90% confidence interval for the mean amount of time that emotionally disturbed patients sleep during a typical night is (6.6, 7.2). Interpret this interval in the context of this problem.
We are 90% confident that the mean hours of sleep that emotionally disturbed patients get on a typical night is in this interval.
A random sample of 3481 post - partum women was taken to determine whether there is a relationship between smoking during pregnancy and birth weight of babies . The researchers found that women who smoked cigarettes during their pregnancy had statistically significantly smaller babies than those who didn't smoke during their pregnancy . Which of the following is a potential lurking variable in this study ?
Whether or not the babies were carried to term or born premature
Sports car owners in a town complain that the state vehicle inspection stations judge their cars differently from sedans. In this state, 72% of all sedans pass inspection on the first time through. In a random sample of 50 sports cars, 34 passed the inspection on their first time through. The state transportation agency wants to use this data to test the claim that the percentage of cars that pass inspection the first time is less than 72%. Are the conditions met to do so?
Yes, because the data was gathered randomly and both np0>/=10 and n(q-p0)>/= 10
A sociologist interested in gender roles wanted to test the claim that women spend more time on housework than men. She randomly sampled 25 heterosexual married couples and recorded the hours spent on housework per week for both female and male in each couple. Are the conditions satisfied to run a Paired t Test?
Yes, because the plots of the differences appear normal with no extreme skew outliers.
If a researcher wanted to increase the power of his test, then he should consider
all of the other answers are correct
Which of the following will NOT increase the power of a hypothesis test?
decreasing the probability of a Type 1 error, α
A recording studio owner in the Dallas area is considering becoming a music producer. His target market is college students in the United States. He randomly selects 25 SMU students from the group of SMU students who attend his church, and he asks the number of hours per month they listen to streaming music services. His findings are given below. What other graph or summary would be appropriate to describe the variables of interest?
measures of center and spread
Sample A: 1, 2, 3, 4, 5, 6, 7 Sample B: 1, 2, 3, 4, 5, 6, 100 Which of the following measures of center will be the same for both samples?
median
