cryingintheclub

For some experiment, the sample space is 𝑆={1,2,3,5,8}. Let 𝑃(1)=0.27, and 𝑃(2)=𝑃(3)=𝑃(5)=0.2 What is 𝑃(8)?

0.13

The 2010 California gubernatorial race pitted Democratic candidate Jerry Brown against Republican candidate Meg Whitman. A TV exit poll used to project the outcome reported that 54.3% of a sample of 3592 voters said they had voted for Jerry Brown. This was a sample from the 9.5 million people who voted in that election. What is the target population? The 3592 voters who were polled All California residents The 1950 who said they voted for Jerry Brown The 9.5 million people who voted

The 9.5 million people who voted

For the previous problem, what is your conclusion? (use a 1% significance level) There is insufficient evidence to conclude that the fuel additive has mean mpg less than the mean mpg without the additive There is sufficient evidence to conclude that the fuel additive has mean mpg less than the mean mpg without the additive Not enough information given to make a conclusion.

There is insufficient evidence to conclude that the fuel additive has mean mpg less than the mean mpg without the additive

Suppose that for a population, the variable of interest is quantitative and is left skewed. Which of the following statements is true? mode = n n > mu We can apply the empirical rule to the data there is no median n < mu

n > mu

Which measure of variability should be used to describe qualitative data? Choose all that apply mode s^2 x bar IQR range none of the above

none of the above

The standard deviation of the probability distribution of a statistic is called the point estimator error of estimation MVUE standard error

standard error

The curve of the probability distribution for a continuous random variable 𝑋 is called the expected value the sample distribution the sampling distribution the probability density function

the probability density function

Suppose you show up at a bus stop to wait for a bus that comes by once every 15 minutes. You do not know what time the bus came by last. The arrival time of the next bus is a uniform distribution with 𝑐=0 and 𝑑=15 measured in minutes. Find the probability that you will wait 5 minutes for the next bus. That is, find 𝑃(𝑋=5).

0

Dentists often use the number of root canals of a smooth canine to estimate the number of patients with that specific canine. Suppose the random variable 𝑋 is the number of smooth canines seen each week. Assume 𝑋 approximately follows a Poisson probability distribution. Assume the average sightings of smooth canine is 2.8. Find the probability that one sighting is made each week.

0.1703

Almost all companies utilize some type of year-end performance review for their employees. Human Resources (HR) at a university's Health Science Center provides guidelines for supervisors rating their subordinates. For example, raters are advised to examine their ratings for a tendency to be either too lenient or too harsh. According to HR, "if you have this tendency, consider using a normal distribution - 10% of employees (rated) exemplary, 20% distinguished, 40% competent, 20% marginal, and 10% unacceptable." Suppose you are rating an employee's performance on a scale of 1 (lowest) to 100 (highest). Also, assume the ratings follow a normal distribution with a mean of 48 and a standard deviation of 13. What is the lowest rating you should give to a "competent" employee if you follow the university's guidelines?

41.24

A researcher applied the carcinogenic (cancer causing) compound benzo(a)pyrene to the skin of five mice, and measured the concentration in the liver tissue after 48 hours. The results (nmol/gm) were as follows: 5.3, 7.4, 5.5, 5.6, 5.5 Determine the mean concentration for these mice.

5.86

Are Americans superstitious? A Harris (Feb.2013) poll of adult Americans was designed to answer this question. One survey item concerned the phrase "see a penny, pick it up, all day long you'll have good luck." The poll found that just one-third of Americans (33%) believe finding and picking up a penny is good luck. Consider a random sample of 22 U.S. adults and let 𝑋X represent the number who believe finding and picking up a penny is good luck. What is the expected value of adults in a sample of size of 22 who believe finding and picking up a penny is good luck?

7.26

For the previous problem, we will

fail to reject 𝐻0H_0 since p-value >𝛼

What measure of variability is the most sensitive to outliers? IQR range mean standard deviation variance

range

Probability quantifies the ______________ in the ______________?

reliability; inference

The Central Limit Theorem tells us that

the sampling distribution of the sample mean can be approximated with a normal distribution for "large"

Which of the following denotes the 75th percentile? 𝑀 𝑄𝐿 𝑥‾‾ 𝑄𝑈

𝑄𝑈

For the previous problem, which of the following conditions must hold in order for the confidence interval to be valid? (Choose all that apply.) The population standard deviation, 𝜎, must be known The sampling distribution of the sample mean must be approximately normal by the central limit theorem 𝑛𝑞ˆ≥15 𝑛𝑝ˆ≥15 a random sample is taken Theorem 6.1 must hold

𝑛𝑞ˆ≥15 𝑛𝑝ˆ≥15 a random sample is taken

For the previous problem, find the value of the test statistic.

𝑡=5.44

From past experience, a wheat farmer living in Manitoba, Canada, finds that his annual profit (in Canadian dollars) is $80,000 if the summer weather is typical, $50,000 if the weather is unusually dry, and $20,000 if there is a severe storm that destroys much of his crop. Weather bureau records indicate that the probability is 0.56 of typical weather, 0.36 of unusually dry weather, and 0.08 for a severe storm. Let 𝑋X denote the farmer's profit next year. Find the expected profit for the farmer next year.

$64,000

In the article "Mediterranean Dietary pattern in a Randomized Trial" ( Archives of Internal Medicine, 1998), 302 survivors of heart attack were put on a Mediterranean diet, rich in vegetables, fruits, and grains. After following these subjects for four years, the authors found that 273 of them were considered healthy. Find a 95% confidence interval for the proportion of all survivors of heart attack who were put on a Mediterranean diet who stay healthy after four years.

(0.871, 0.937)

Instruments used to measure physical characteristics do not give the same value every time they're used. The measurements vary. Suppose a person was weighed on a scale 13 times. The mean of these measurements is 155.99 pounds with a standard deviation of 0.209 pounds. Also, suppose we know from the manufacturer of the scale that the measurements vary by 0.2 pounds on average (that is, 𝜎=0.2) and they are normally distributed. Calculate a 90% confidence interval for the mean weight of this person. (Round to four decimal places but be careful not round until the last step)

(155.899, 156.081)

In a study on the physical activity of young adults, pediatric researchers measured overall physical activity as the total number of registered movements (counts) over a period of time and then computed the number of counts per minute (cpm) for each subject. The study revealed that the overall physical activity of obese young adults has a mean of 𝜇=326 cpm and a standard deviation of 𝜎=77 cpm. In a random sample of 𝑛=100 obese young adults, consider the sample mean counts per minute, 𝑥‾‾\bar x. What is the probability that the mean overall physical activity level of the sample is greater than 345 cpm?

0.0068

Suppose that a left-tailed hypothesis test for 𝜇 results in the test statistic 𝑡=−2.165which follows a Student's 𝑡-distribution with 13 degrees of freedom. Approximate the p-value for this test using the Student's 𝑡t table. p-value>0.10 p-value=0.025 p-value=0.015 0.01<p-value<0.025 0.025<p-value<0.05

0.01<p-value<0.025

Suppose 𝑋 is normally distributed with mean 27 and variance 4. Find the probability that 𝑋 is greater than 31.

0.0228

In kidney transplantations, compatibility between donor and receiver depends on such factors as blood type and antigens. Suppose that for a randomly selected donor from a large national kidney registry, there is a 7% chance that he or she is compatible with a specific receiver. A sample of size 4 donors are randomly selected from this registry. Find the probability that exactly 2 of the selected donors is compatible.

0.0254

Suppose there is a 0.153 probability that a randomly selected person aged 35 years or older is a jogger. In addition, there is a 0.244 probability that a randomly selected person aged 35 years or older is female, given that he or she jogs. What is the probability that a randomly selected person aged 35 years or older is female and jogs?

0.037

A random sample of 𝑛=290 measurements is drawn from a binomial population with probability of success 0.82. Find the probability that the sample proportion is greater than 0.86.

0.0384

A car dealership (which is opened 7 days a week) sells an average of 5 cars in a day. Assume the number of cars sold each day is independent from any other day. The number of cars sold on any given day can be approximated with a Poisson distribution. Find the probability that the car dealership will sell 7 cars tomorrow.

0.1044

In the paper "Diagnostic efficiency of home pregnancy test kits: a meta-analysis" by Bastian et al. (Archives of Family Medicine, 1998), the researchers examined the accuracy of several pregnancy tests. One of the tests was the e.p.t.~plus pregnancy test. For this test, it gave a positive result (it found the user was pregnant) 90% of the time for those who were actually pregnant. If the user was not pregnant, it gave a positive result only 8% of the time. There were about 110 pregnancies per 1,000 women ages 15-44 in the United States in 1998. Use this as the percentage of pregnancies in the population. If an individual is randomly selected from the target population and takes the pregnancy test, what is the probability that the test is positive? (Round your answer to 4 decimal places)`

0.1702

The manager of a local soft-drink bottling company believes that when a new beverage-dispensing machine is set to dispense 7 ounces, it in fact dispenses an amount 𝑋X at random anywhere between 6.5 and 7.5 ounces, inclusive. Suppose 𝑋X has a uniform probability distribution. Find the probability that a randomly selected bottle filled from this machine will have less than 6.73 ounces?

0.23

Suppose 𝑃(𝐴)=0.3, 𝑃(𝐵)=0.23, and 𝑃(𝐴∩𝐵)=0.06. What is 𝑃(𝐴∪𝐵)?

0.47

For the previous problem, If a randomly selected individual is tested and the result is positive, what is the probability that the individual is pregnant? (Round your answer to 4 decimal places)

0.5817

Each year, more than 1 million heart patients undergo an angioplasty. The benefits of an angioplasty were challenged in a recent study of 2,287 patients (207 Annual Conference of the American College of Cardiology, New Orleans). All the patients had substantial blockage of the arteries, but were medically stable. All were treated with medication such as aspirin and beta blockers. However, half the patients were randomly assigned to get an angioplasty and half were not. After five years, the researchers found that 211 of the 1,145 patients in the angioplasty group had subsequent heart attacks, compared with 202 of 1,142 patients in the medication-only group. We want to test to see if there is enough evidence to conclude that there is a difference in the rate of heart attacks for the two groups at 𝛼=0.10\alpha=0.10. The value of the test statistic is 0.46. Find the p-value for this test.

0.6456

Suppose 𝑋∼Bin(9, 0.58). Find the population standard deviation.

1.481

The S-B test measures intelligence quotient (IQ) and has a mean of 102 with a standard deviation of 18 for all adults. The newer W-A Intelligent Scale (WAIS) has a mean of 104 with a standard deviation of 17. If someone takes the WAIS test and scores a 138, this would be equivalent (in relative standing) to what IQ on the S-B scale?

138

For the data in the previous problem, what is the value for the upper inner fence (the upper boundary for outliers)?

17.75

SAT verbal scores have a bell-shaped distribution with a mean of 448 and a standard deviation of 92. What percent of these scores lie between 448 and 540?

34%

A common biology experiment involves growing radish seedlings under various conditions. In one version of this experiment, a moist paper towel is put into a plastic bag. Staples are put in the bag about one-third of the way from the bottom of the bag and then radish seeds are placed along the staple seam. One group of students kept their radish seed bags in constant light for three days and then measured the length, in mm, of each radish shoot at the end of the three days. A boxplot of their measurements is given below. outliars at 20/21 𝑄𝐿=6.5Q_L=6.5, 𝑀=9.5M=9.5, 𝑄𝑈=11Q_U=11 What is the IQR

4.5

Suppose the diameters of a new species of apple have a mound-shaped, symmetric distribution with mean of 9.94 cm and a variance of 4 cm^2. Using the empirical rule, what percentage of apples have diameters that are between 5.94 cm and 13.94 cm?

About 95%

True or False: A disadvantage of using a 99 percent confidence level rather than a 95 percent confidence level is that larger samples must be taken for establishing higher levels of confidence.

False

True/False: If events 𝐴1 and 𝐴2 are mutually exclusive, then they must also be complements of each other.

False

True/False: If the null hypothesis is favored over the alternative hypothesis, the data is statistically significant.

False

True/False: If we conclude the null hypothesis is true when in fact the null hypothesis is false, that is called a type I error.

False

True/False: The Central Limit Theorem states that a sufficiently large population size indicates the population distribution is approximately normal.

False

True/False: Two events that are mutually exclusive can also be independent.

False

When estimating some parameter with a point estimator, we want the point estimator that is the MVUE. What does MVUE stand for?

Minimum Variance Unbiased Estimator

A sample of 𝑛=8 automobiles was selected, and each was subjected to a 5-mph crash test. Denoting a car with no visible damage by S (for success) and a car with such damage by F, results were as follows: S S F F F S S S What measure of central tendency would be appropriate for this data? mode mean variance upper quartile median

Mode

Which of the following is NOT considered a measure of variability? Choose all that apply. standard deviation IQR 𝜎2\sigma^2 mode range

Mode

For the previous problem, make the appropriate conclusion.

Reject 𝐻0H_0. There is sufficient evidence to conclude that the true mean heart rate during laughter exceeds 71 beats per minute.

For a normal distribution with 𝜇=0 and 𝜎=1, it is called the uniform distribution the standard deviation Student's 𝑡 distribution the standard normal distribution the sampling distribution

The standard normal distribution

Suppose you are conducting an hypothesis tests for the difference between the means of two populations. You find the p-value is 0.61. What would be an appropriate way to interpret this result if 𝛼=0.05? (Choose all that apply) The means of the two populations are the same. The means of the two populations are not different. There is enough evidence to conclude that there is a difference between the means of the two populations. There is enough evidence to conclude that the means of the two populations are the same. There is not enough evidence to conclude that the means of the two populations are different. There is not enough evidence to conclude that the means of the two populations are the same.

There is not enough evidence to conclude that the means of the two populations are different.

True or False: A disadvantage of using a 99 percent confidence level rather than a 95 percent confidence level is that larger samples must be taken for establishing higher levels of confidence.

True

Let 𝐴 and 𝐵 be events so that 𝑃(𝐴)=0.13, 𝑃(𝐵)=0.07, and 𝑃(𝐴∪𝐵)=0.2. Are 𝐴 and 𝐵 mutually exclusive? How do you know? Yes, because 𝑃(𝐴∩𝐵)=0 No, because 𝑃(𝐴)>𝑃(𝐵) No, because 𝑃(𝐴∪𝐵)≥0 Yes, because 𝑃(𝐴)>𝑃(𝐵) Not enough information given to answer the question

Yes, because 𝑃(𝐴∩𝐵)=0

For the previous problem, which of the following conditions must hold in order for your conclusion to be valid? (Choose all that apply) The cars with the additive must be independent from the cars without the additive 𝑛𝑝ˆ≥15 a random sample is taken The central limit theorem holds 𝑛𝑞ˆ≥15 Theorem 6.1 must hold

a random sample is taken Theorem 6.1 must hold

Six mice were randomly selected and injected with a dose of a drug to see how it affects their reaction time. After injection, each mouse was put into a maze and the time it take the mouse to get through the maze was recorded (in seconds). What is the population? all mice the drug dose the maze reaction time the sampled mice

all mice

Pairing samples may reduce the variability but also reduces what? the difference in the mean degrees of freedom the value of the test statistic the probability of making a type I error

degrees of freedom

Which of the following is a random variable? (choose all that apply) 𝑛 𝜎𝑥‾‾ s^2 𝑝p 𝜇 𝑝ˆ

s^2 𝑝ˆ

The probability distribution of a statistic is called the probability density function sampling distribution standard error expected value

sampling distribution

In developing a new gasoline additive, researchers randomly select 10 cars and drive them both with and without the additive. The sample mean difference in gas mileage (mpg with additive - mpg without additive) is 0.41 mpg with a sample variance of 0.16. Assume the differences are from an approximately normal distribution. We want to test the hypothesis that the fuel additive has mean mpg less than the mean mpg without the additive. Calculate the test statistic.

t=3.24

The p-value is the probability that 𝐻0 is true. the probability that 𝐻𝑎 is true. the probability of obtaining the test statistic or more in favor of 𝐻𝑎 if 𝐻0 is true. the probability of obtaining the test statistic or more in favor of 𝐻0 if 𝐻𝑎 is true.

the probability of obtaining the test statistic or more in favor of 𝐻𝑎 if 𝐻0 is true.

The Central Limit Theorem tells us that the sampling distribution of the sample mean can be approximated with a normal distribution for "large" 𝑛 You Answered as 𝑛 gets bigger, the sample data becomes more like the normal distribution if the data comes from an (approximately) normally distributed population, then the sample mean will also be (approximately) normally distributed the minimum variance unbiased estimator is the "best" estimator for a parameter

the sampling distribution of the sample mean can be approximated with a normal distribution for "large" 𝑛

Myocardial blood flow (MBF) was measured for two groups of subjects after 5 minutes of bicycle exercise. The normoxia (normal oxygen") group was provided normal air to breath whereas the hypoxia group was provided with a gas mixture with reduced oxygen, to simulate high altitude. The results (in ml/min/g) were analyzed in StatCrunch for which the output is below. The researchers are interested in seeing if the normoxia group has a reduced mean MBF as compared to the hypoxia group at the 5% significance level. Let the normoxia group be the first population and let the hypoxia group be the second population. Assume both samples come from normally distributed populations with equal variances.

𝐻0:𝜇1−𝜇2=0 𝐻𝑎:𝜇1−𝜇2<0

Two groups of children were shown a commercial. One group (the video-only group) was shown only the video portion of the commercial; the second group (the A/V group) was shown the ad with both audio and video. Following the viewing, the children were asked to recall 10 specific items from the ad. The researchers theorized that children who received a video only presentation will have a mean recall of ad information lower than those who receive the both audio and video aspects of the ad. Let population 1 be the video-only group and population 2 be the A/V group. The sample sizes were 𝑛1=10n_1=10 and 𝑛2=6. Use 𝛼=0.05. Assume 𝜎21≠𝜎22 and the samples are from approximate normally distributed populations. Setup the hypotheses for this problem.

𝐻0:𝜇1−𝜇2=0 𝐻𝑎:𝜇1−𝜇2<0

Researchers investigated the physiological changes that accompany laughter. Seventy subjects watched film clips designed to evoke laughter. During the laughing period, the researchers measured the heart rate of each subject, with the following summary results: 𝑥‾‾=73.6, 𝑠=4. It is well known that the mean resting heart rate of adults is 71 beats per minute. Set up 𝐻0 and 𝐻𝑎for testing whether the true mean heart rate during laughter exceeds 71 beats per minute.

𝐻0:𝜇=71 𝐻𝑎:𝜇>71

Which of the following implies events A and B are independent? 𝑃(𝐴∩𝐵)=𝑃(𝐴|𝐵)𝑃(𝐵) 𝑃(𝐴∩𝐵)=0 𝑃(𝐴|𝐵)=𝑃(𝐵|𝐴) 𝑃(𝐴|𝐵)=𝑃(𝐴∩𝐵) 𝑃(𝐴∩𝐵)=𝑃(𝐴)𝑃(𝐵) 𝑃(𝐴|𝐵)=𝑃(𝐴)𝑃(𝐵)

𝑃(𝐴∩𝐵)=𝑃(𝐴)𝑃(𝐵)

Suppose for the hypotheses 𝐻0:𝑝=0.3 𝐻𝑎:𝑝>0.3 we find a test statistic of 1.77 and a p-value of 0.0384. Which of the following probability statements represents the p-values?

𝑃(𝑍≥1.77)=0.0384

Which of the following are continous random variables? (Choose all that apply) 𝑋∼𝑁(𝜇,𝜎) 𝑋∼𝐵𝑖𝑛(𝑛,𝑝) Standard normal random variable 𝑍 𝑋∼𝑃𝑜𝑖𝑠(𝜆) 𝑋∼𝑈(𝑐,𝑑)

𝑋∼𝑁(𝜇,𝜎) Standard normal random variable 𝑍 𝑋∼𝑈(𝑐,𝑑)

For the previous problem, if 𝛼=0.01, find the rejection region for the test.

𝑡>2.382

What is the correct notation for the population median? 𝜂 sigma mu M x bar s^2

𝜂