Stats exam 1 review

Seventy percent of the light aircraft that disappear while in flight in a certain country are subsequently discovered. Of the aircraft that are discovered, 60% have an emergency locator, whereas 90% of the aircraft not discovered do not have such a locator. Suppose that a light aircraft has disappeared. If it has an emergency locator, what is the probability that it will not be discovered?

0.067

In your sock drawer, you have 4 blue, 5 grey, and 3 black socks. Half asleep one morning, you grab 2 socks at random and put them on. What is the probability you are wearing matching socks?

0.288

A professional basketball player is a poor free-throw shooter. Consider situations in which he shoots a pair of free throws. The probability that he makes the first free throw is 0.51. Given that he makes the first, suppose the probability that he makes the second is 0.59. Given that he misses the first, suppose the probability that he makes the second one is 0.36. What is the probability that he makes one of the two free throws?

0.3855

Given the probabilities shown below, what is P(A⋂B)? P(A) = 0.65, P(B) = 0.32, and P(B|A) = 0.75

0.4875

1380 randomly sampled registered voters from Tampa, Florida were asked if they thought workers who have illegally entered the US should be (i) allowed to keep their jobs and apply for US citizenship, (ii) allowed to keep their jobs as temporary guest workers but not allowed to apply for US citizenship, or (iii) lose their jobs and have to leave the country. The results of the survey by political ideology are shown below. What percent of these Tampa, Florida voters who identify themselves as conservatives are also in favor of the citizenship option?

20.0%

Suppose you have a data set with the following five-number summary: Minimum = 26, Q1 = 32, Median = 34, Q3 = 38, Maximum = 58. What is the lower cutoff point for potential outliers? (By lower cutoff point, we mean the number such that anything smaller than it is an outlier).

23

Jim is conducting a health survey of residents of Brazos County. He asks them their age, gender, height, weight, type of insurance, marital status, income, and the number of days they were sick in the last month. The possible values for marital status are married, widowed, divorced/separated, single/never married, and living with a partner but not married. How many of the variables in the health survey were categorical and how many were numeric?

3 categorical and 5 numerical.

The boxplot below shows the distribution of heights of 16 undergraduate statistics students. Using this boxplot, approximately how many students are 69 inches or taller?

4

A researcher is interested in learning how often college students watch TV. They randomly select 500 college students and ask, "In the past seven days, how many days did you watch television?" The random variable X represents the number of days an individual watched television. The probability distribution below shows the results of the survey. What is the expected value of X?

5.44

Below is a histogram of the IQ ("intelligence quotient") scores of 60 fifth-grade students chosen at random from one school. The range is defined as the maximum minus the minimum. What is the range of this distribution?

80

Eli wants to determine whether or not there is an association between gender and GPA among high school seniors in Ohio. He randomly selects 100 high school seniors at Amelia High School, a public school in southwest Ohio. He asks them to report their gender, as well as their current GPA. Out of these 100 students, 57 were female and 43 were male. The average GPA of the 57 female high school seniors was 3.47. What is the population in this study?

All high school seniors in Ohio.

Which of the following is a reason why a researcher may choose to use a cluster sample?

Because it is impossible or not feasible to take a simple random sample or because the researcher cannot get a list of every individual in the population.

A researcher wants to determine if a new exercise program helps people lose weight. She recruits over 1200 subjects (her statistician determined this number from sample size calculations) and randomly assigns them to either participate in the new exercise program or no exercise program. She tells those in the new program group to exercise 3 times a week and tells those in the no exercise group that they should not exercise for the duration of the study. Based on this information, which of the following principles of experimental design is NOT present in this study? A)Randomization. B)Control/Placebo. C)Replication/Sample Size. D)Blinding.

Blinding.

In which of the following study designs would you generally know the value of the parameter?

Census

A researcher wants to determine if a new flu vaccine protects people from the flu better than the current vaccine. He has 100 subjects for his study. He believes that sex will affect how well the vaccine works, so within these 100 subjects, splits them up into males (48 subjects) and females (52 subjects). Within each sex, he randomly assigns half of the subjects to get the new flu vaccine and the other half to get the current flu vaccine. What type of study design is this?

Experimental Study: Block Design.

Consider the population of all students at your school. A certain proportion support removing vending machines. Your friend randomly samples 20 students from the​ school and uses the sample proportion who support removing vending machines to predict the population proportion at the school. You take your​ own separate random sample of 20 ​students and find the sample proportion that supports removing vending machines. How likely is it that the sample proportions are the​ same?

It is unlikely that the sample proportions will be exactly the same.​ However, they should be close to each other because the samples represent the same population.

Multiple myeloma is a cancer of the bone marrow currently without an effective cure. It affects primarily older individuals: It is almost never diagnosed in individuals under 40 years old, and its incidence rate (the number of diagnosed malignant cases per 100,000 individuals in the population) is highest among individuals 70 years of age and older. If you were to create a histogram to show the distribution of the incidence rate of multiple myeloma by age at diagnosis, how would you describe its skewness?

LEFT SKEWED

Consider the following measures that can be used to describe a data set: mean, median, IQR, and standard deviation. Which of these following describes all the values that are not robust?

Mean and Standard Deviation.

For the distribution shown below, which point represents the mean and which point represents the median

Mean: Point B, Median: Point B.

Because of the increasing nuisance of spam email messages, many start-up companies have emerged to develop e-mail filters. One such filter was recently advertised as being 81% accurate. This could mean one of four things. One thing it could mean is that 81% of valid email is allowed through. Let S denote the event that the message is spam and let B denote the event that the filter blocks the message. Which of the following expresses the statement, "81% of valid email is allowed through," as a conditional probability?

P(Bc|Sc) = 0.81.

Which of the following is an example of a voluntary response sample?

Radio asks people listening to call in and say whether or not they want a new stoplight at a busy intersection.

A researcher wants to know more about the resting pulse rate of high school aged children. She takes a random sample of 17 students at a local high school and measures their resting pulse rate. The boxplot below depicts the five-number summary for her data set. Based on this boxplot, what is the skewness of the data set?

Right Skewed.

Given the following situations, when would you use a histogram?

Showing the distribution of the GPA's of all of the students at Texas A&M.

Taylor Swift is interested in learning what proportion of her fans watched her premiere Betty live at the ACM Awards on September 16, 2020. She takes a simple random sample of 400 fans and asks them. Of the 400 fans, 382 of them (95.5%) respond that they watched her perform. What is the statistic and what is its value?

The statistic is the proportion of the sampled Taylor Swift fans who watched the performance, which is 0.955.

A certain region has a population of 6.5 million. On any given day (excluding days like today where there is a pandemic and we aren't supposed to leave our houses), the probability that a randomly selected resident decides to visit the amusement park is 1/5000. Assume that each resident's decision to visit is independent of the other residents. What is the probability that all the residents of this region will decide to go to the amusement park tomorrow (assuming the amusement park is open tomorrow)?

Very close to zero