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Statistics STA 2023 Midterm Review, Exams of Statistics

A review guide for a statistics midterm exam covering topics from tests 1, 2, and 3. It includes a variety of questions and problems related to statistical concepts such as parameters vs. Statistics, data collection methods, probability distributions, the normal distribution, and the central limit theorem. The document seems to be intended for students enrolled in a statistics course at the university level, likely in the 2023 academic year. The questions cover a range of statistical topics and could be useful for students as study notes, lecture notes, or practice problems to prepare for the midterm exam.

Typology: Exams

2024/2025

Available from 10/14/2024

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Statistics STA 2023 Midterm Review (Tests 1, 2, 3)
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16
1. Which of the following correctly describes the
rela- tionship between a parameter and a statistic?
2. A study was done to determine the average
commute time per week to and from class for an
SPC student attending a lecture class. For
convenience, a sample of 60 students was taken by
randomly selecting a lecture class on the Gibbs
campus (30 students), and also a lecture class on
the Clearwater campus (30 students). The students
selected for the sample were then asked where they
were commuting from, when, and how often. The
information was then entered into a GPS system in
order to obtain estimated commuting times. Identify
the population.
3. Which branch of statistics deals with the
organization and summarization of collected
information?
4. From past figures, it is predicted that 19% of the
regis- tered voters in California will vote in the June
primary. Identify whether the statement describes
inferential statistics or descriptive statistics.
5. The cost of a Statistics textbook. Classify the
variable as qualitative or quantitative.
6. Eye Color. Classify the variable as qualitative or
quan- titative.
7. A study where a drug was given to 23 patients and a
placebo to another group of 23 patients to determine
if the drug has an effect on a patient's illness. Decide
which method of data collection you would use to
collect data for the study. Specify either
observational study, experiment, simulation, or
survey.
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Statistics STA 2023 Midterm Review (Tests 1, 2, 3)

1 /

  1. Which of the following correctly describes the rela- tionship between a parameter and a statistic?
  2. A study was done to determine the average commute time per week to and from class for an SPC student attending a lecture class. For convenience, a sample of 60 students was taken by randomly selecting a lecture class on the Gibbs campus (30 students), and also a lecture class on the Clearwater campus (30 students). The students selected for the sample were then asked where they were commuting from, when, and how often. The information was then entered into a GPS system in order to obtain estimated commuting times. Identify the population.
  3. Which branch of statistics deals with the organization and summarization of collected information?
  4. From past figures, it is predicted that 19% of the regis- tered voters in California will vote in the June primary. Identify whether the statement describes inferential statistics or descriptive statistics.
  5. The cost of a Statistics textbook. Classify the variable as qualitative or quantitative.
  6. Eye Color. Classify the variable as qualitative or quan- titative.
  7. A study where a drug was given to 23 patients and a placebo to another group of 23 patients to determine if the drug has an effect on a patient's illness. Decide which method of data collection you would use to collect data for the study. Specify either observational study, experiment, simulation, or survey.

Statistics STA 2023 Midterm Review (Tests 1, 2, 3)

2 / A statistic is calcu- lated from sample data and is gener- ally used to esti- mate a parameter. All SPC students who attend lecture classes. descriptive inferential quantitati ve qualitativ e experime nt

Statistics STA 2023 Midterm Review (Tests 1, 2, 3)

4 / systematic cluster convenience 47% 71 72

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  1. The heights (in inches) of ten randomly chosen Amer- ican males are shown below. Find the mode. 71 67 67 72 76 72 73 68 72 72
  2. The median LSAT score reported by a Law School is
    1. Which of the following is not correct?
  3. The ages of a group of patients being treated at one hospital for osteoporosis are summarized in the fre- quency histogram below. Identify the overall shape of the distribution and determine whether the mean or the median would provide a better measure of center.
  4. Here are costs (in dollars) of 12 electric smooth top ranges. Find the range of the data set.
  5. The heights (in inches) of ten randomly chosen Ameri- can males are shown below. Find the sample standard deviation. 71 67 67 72 76 72 73 68 72 72
  6. Which of the three histograms shown summarizes the data set with the smallest standard deviation?
  7. Lengths of pregnancies of humans are normally dis- tributed with a mean of 265 days and a standard devi- ation of 10 days. Use the Empirical Rule to determine

7 / 16 the percentage of women whose pregnancies are be- tween 255 and 275 days.

  1. The heights (in inches) of ten randomly chosen Amer- ican males are shown below. Determine the Five Num- ber Summary of the data set. 71 67 67 72 76 72 73 68 72 72
  2. The age at which a person purchased a new BMW is summarized in the following boxplot. For which series was the median age of purchase equal to 41?
  3. A high school student took two college entrance ex- ams and scored 1120 on the SAT and 27 on the ACT. Suppose that SAT scores have a mean of 950 and a standard deviation of 140 while the ACT scores have a mean of 22 and a standard deviation of 4. Assuming the performance on both tests follows a normal dis- tribution, determine which test the student did better on.
  4. What is the set of all possible outcomes of a probabil- ity experiment?
  5. If the computed probability of an event occurring is 0.01. Which of the following statements is correct?
  6. A probability cannot be negative or greater than
    1. True or False.
  7. If the probability of an event is 1, the event is impos- sible. True or False.
  8. The probability of an individual having Type O blood is 0.45. What is the probability of having a blood type other than O?

The 5 series ACT sample space We would expect the event to occur about one percent of the time True Fals

  • 8 /
  • e 0.

10 / show that about 42% of Americans voted in the previous national election. If three Americans are

11 / randomly selected, what is the probability that none of them voted in the last election?

  1. If a person is selected at random, decide if the events A and B are mutually exclusive or not mutually exclu- sive. A: Their birthday is in the fall. B: Their birthday is in October.
  2. A survey revealed that 31% of people are entertained by reading books, 39% are entertained by watching TV, and 30% are entertained by both books and TV. What is the probability that a person will be entertained by either books or TV?
  3. A survey of senior citizens at a doctor's office shows that 52% take blood pressure-lowering medication, 43% take cholesterol-lowering medication, and 5% take both medications. What is the probability that a senior citizen takes either blood pressure-lowering or cholesterol-lowering medication?
  4. A card is drawn from a standard deck of 52 playing cards. Find the probability that the card is an ace or a black card.
  5. The distribution of Master's degrees conferred by a university is listed in the table. (assume that a student majors in only one subject) What is the probability that a randomly selected stu- dent with a Master's degree majored in English or Mathematics? Round your answer to three decimal places.
  6. The following table categorizes the students in a first-grade class by age and gender. What proportion of the students are female or less than 6 years old? not mutually exclu- sive
    7/
    10/

13 /

  1. For a normal curve with mean 8 and standard devi- ation 7, identify which of the following intervals will define an area underneath the curve of approximately 0.
  2. If X is a normal random variable with a mean of 20 and standard deviation of 2, which of the following could be the graph of the distribution of X?
  3. Find the area of the indicated region under the stan- dard normal curve.
  4. Find the area under the standard normal curve be- tween z = 0 and z = 3.
  5. Find the area under the standard normal curve to the right of z = 1.
  6. Find the area under the standard normal curve to the left of z = 1.5.
  7. Use the standard normal distribution to find P(-2. < z < 0).
  8. Use the standard normal distribution to find P(-2. < z < 1.50).
  9. For the standard normal curve, find the z-score that corresponds to the third quartile. Identify the z- score corresponding to the indicated percentile.
  10. An airline knows from experience that the distribution of the number of suitcases that get lost each week on a certain route is approximately normal with ¼ = 15. from 1 to 15 D.
    and à = 3. 6 W. hat is the probability that during a given week the airline will lose less than 20 suitcases?

14 /

  1. An airline knows from experience that the distribution of the number of suitcases that get lost each week on a certain route is approximately normal with ¼ = 15.

and à = 3. 6 W. hat is the probability that during a given week the airline will lose more than 20 suitcases?

  1. An airline knows from experience that the distribution of the number of suitcases that get lost each week on a certain route is approximately normal with ¼ =

15.5 and à = 3. 6 W. hat is the probability that during a given week the airline will lose between 10 and 20 suitcases?

  1. Assume that the heights of American men are normal- ly distributed with a mean of 69.0 inches and a stan- dard deviation of 2.8 inches. The U.S. Marine Corps requires that men have heights between 64 and 78 inches. Find the percent of men meeting these height requirements.
  2. The heights of women are normally distributed with a mean of 65 inches and a standard deviation of 2.5 inches. The heights of men are also normal with a mean of 70 inches. Approximately what percent of women are taller than a man of average height?
  3. A tire company finds the lifespan for one brand of its tires is normally distributed with a mean of 47, miles and a standard deviation of 3000 miles. If the manufacturer is willing to replace no more than 10% of the tires, what should be the approximate number of miles for a warranty?
  4. The probability distribution of the sample mean is called the:
  5. As the sample size becomes larger, the sampling dis- tribution of the sample mean approaches a

16 / The Central Limit Theorem may be used to conclude that the sampling distribution of means for any popu- lation is approximately normal provided that:

  1. Which of the following statements explains the follow- ing graphic, which includes a picture of a distribution along with three sampling distributions of the mean with different sample sizes:
  2. If the standard deviation of a population is 20 and we take a sample of size 16 from which to calculate a mean, the standard error (the standard deviation of the sample mean) is:
  3. The average number of pounds of red meat a person consumes each year is 196 with a standard deviation of 22 pounds (Source: American Dietetic Association). If a sample of 50 individuals is randomly selected, find the probability that the mean of the sample will be less than 200 pounds.
  4. Assume that the salaries of elementary school teach- ers in the United States are normally distributed with a mean of $32,000 and a standard deviation of $3000. If 100 teachers are randomly selected, find the proba- bility that their mean salary is greater than $32,500.
  5. The average number of pounds of red meat a person consumes each year is 196 with a standard deviation of 22 pounds (Source: American Dietetic Association). If a sample of 50 individuals is randomly selected, find the probability that the mean of the sample will be greater than 200 pounds. the sample size is 30 or more Averages calculat- ed from larger samples will be less variable. 5