**Introduction of Statistics 200**

**STAT 200 **

**1. What is the BEST measure of the central tendency for the following set of numbers:**

**18, 34, 56, 67, 875**

a. Mean

b. Median

c. Mode

d. Standard Deviation

e. None of above

**2. Which of the following is/are measure(s) of variability? (select all that apply)**

a. mean

b. range

c. mode

d. variance

e. linear transformation

**3. For a set of numbers, if the mean is equal to the median, its distribution might be:**

a. Right-skewed

b. Left-skewed

c. Normally distributed

d. Positively-skewed

**4. In the graph, there are two distrubitions and we can tell (check all that apply):**

a. The mean of distribution A> the mean of distribution B

b. The mean of distribution A < the mean of distribution B

c. The standard deviation of distribution A> the std deviation of distribution B

d. The standard deviation of distribution A= the st deviation of distribution B

**5. Which of the following can measure variability? (Select all that apply**)

a. mean

b. median

c. range

d. variance

e. standard deviation

f. Interquartile range

**6. A researcher collected BMI (Body Mass Index) of 50 students in an Engineering school. He found the mean BMI was much smaller than the median BMI. The reason for this might be: **

a. Several students had much smaller BMI scores than the other students

b. Several students had much larger BMI scores than the rest

c. The researcher made some measurement errors

d. All the students had smaller BMI scores, compared to national average

**7. There are 20 coupons rolled up and placed inside round plastic balls in a box. There are 3 different types of coupons: 10 of them can be redeemed for “free drinks”, 5 can be redeemed for “free desserts”, and 5 can be redeemed for “free entrees”. If you shake the box and then randomly select one coupon. What’s the probability that you will get a free entree coupon? **

**8. Mary was tossing a coin. She tossed three times. What’s the probability that at the first toss she gets a head, the second toss she gets a tail at and the third time she get a tail? **

**9. Alice tossed a six-sided die three times. What’s the probability that she gets ones on all three throws? **

**10. Imagine a city with 50,000 people. Twenty percent of the population consists of children younger than five years of age. For the children under five years old, the base rate of malnutrition is 6%. How many children under five years of age in that city are malnourished? **

**11. Which of the following pairs are NOT independent events?**

a. Flipping a coin twice

b. Throwing a die twice

c. Drawing a heart from a set of pokers card, putting it back, and then drawing another heart.

d. Drawing a heart from a set of pokers card, not putting it back and then drawing a diamond.

**12. Consider a normal distribution with a mean of 20 and standard deviation of the mean of 6. 68% of its area is within: **

a. One standard deviation of the mean

b. Two standard deviations of the mean

c. Three standard deviations of the mean

d. It depends on the value of the mode

**13. A normal distribution with a mean of 10 and standard deviation of 5. What is the corresponding Z score for a case having a value of 7? **

**14. Consider a normal distribution with a mean of 5 and standard deviation of 4. Approximately, what proportion of the area lies between values of -3 and 13. **

a. 95%

b. 68%

c. 99%

d. 50%

**15. A binomial distribution is a probability distribution for ____ events for which there are ___ possible outcomes**

a. Independent; two

b. Dependent; two

c. Independent; multiple

d. Dependent; Multiple

**16. If we want to estimate the average height of students in an elementary school, which of the following situations can certainly cause bias in our estimation?**

a. If the rulers we use systematically overestimate the students’ heights

b. If we only sample the female students in that elementary school

c. If we use random sampling method to select students

d. If we only selected students who were eager to participate in the study

**17. The sampling variability of a statistic refers to how much the statistic varies from sample to sample and is usually measured by its:**

a. standard error

b. standard deviation

c. average

d. median

**18. A graduate school Professor wanted to know average age of students in his class. He randomly selected five students and obtained their ages. Their ages were 26, 32, 22, 21, and 25 years. What’s the standard error of the mean from our sample estimation? **

**19. Which of the assumption is NOT required to compute a confidence interval for the difference between two means? **

a. The two populations have the same variance.

b. The populations are normally distributed.

c. Each value is sampled independently from each other value.

d. The two populations have the similar means.

**20. For a t distribution with 1,000 degrees of freedom, 99% of the distribution is within how many standard deviations of the mean? **

a. One

b. Two

c. Three

d. Four

**1.**

**6.**

**11.**

**16.**

**2.**

**7.**

**12.**

**17.**

**3.**

**8.**

**13.**

**18.**

**4.**

**9.**

**14.**

**19.**

**5.**

**10.**

**15.**

**20.**

**CALCULATIONS (SHOW PROBLEM NUMBER)**

**Introduction of Statistics 200**

**STAT 200 **

**1. What is the BEST measure of the central tendency for the following set of numbers:**

**18, 34, 56, 67, 875**

a. Mean

b. Median

c. Mode

d. Standard Deviation

e. None of above

**2. Which of the following is/are measure(s) of variability? (select all that apply)**

a. mean

b. range

c. mode

d. variance

e. linear transformation

**3. For a set of numbers, if the mean is equal to the median, its distribution might be:**

a. Right-skewed

b. Left-skewed

c. Normally distributed

d. Positively-skewed

**4. In the graph, there are two distrubitions and we can tell (check all that apply):**

a. The mean of distribution A> the mean of distribution B

b. The mean of distribution A < the mean of distribution B

c. The standard deviation of distribution A> the std deviation of distribution B

d. The standard deviation of distribution A= the st deviation of distribution B

**5. Which of the following can measure variability? (Select all that apply**)

a. mean

b. median

c. range

d. variance

e. standard deviation

f. Interquartile range

**6. A researcher collected BMI (Body Mass Index) of 50 students in an Engineering school. He found the mean BMI was much smaller than the median BMI. The reason for this might be: **

a. Several students had much smaller BMI scores than the other students

b. Several students had much larger BMI scores than the rest

c. The researcher made some measurement errors

d. All the students had smaller BMI scores, compared to national average

**7. There are 20 coupons rolled up and placed inside round plastic balls in a box. There are 3 different types of coupons: 10 of them can be redeemed for “free drinks”, 5 can be redeemed for “free desserts”, and 5 can be redeemed for “free entrees”. If you shake the box and then randomly select one coupon. What’s the probability that you will get a free entree coupon? **

**8. Mary was tossing a coin. She tossed three times. What’s the probability that at the first toss she gets a head, the second toss she gets a tail at and the third time she get a tail? **

**9. Alice tossed a six-sided die three times. What’s the probability that she gets ones on all three throws? **

**10. Imagine a city with 50,000 people. Twenty percent of the population consists of children younger than five years of age. For the children under five years old, the base rate of malnutrition is 6%. How many children under five years of age in that city are malnourished? **

**11. Which of the following pairs are NOT independent events?**

a. Flipping a coin twice

b. Throwing a die twice

c. Drawing a heart from a set of pokers card, putting it back, and then drawing another heart.

d. Drawing a heart from a set of pokers card, not putting it back and then drawing a diamond.

**12. Consider a normal distribution with a mean of 20 and standard deviation of the mean of 6. 68% of its area is within: **

a. One standard deviation of the mean

b. Two standard deviations of the mean

c. Three standard deviations of the mean

d. It depends on the value of the mode

**13. A normal distribution with a mean of 10 and standard deviation of 5. What is the corresponding Z score for a case having a value of 7? **

**14. Consider a normal distribution with a mean of 5 and standard deviation of 4. Approximately, what proportion of the area lies between values of -3 and 13. **

a. 95%

b. 68%

c. 99%

d. 50%

**15. A binomial distribution is a probability distribution for ____ events for which there are ___ possible outcomes**

a. Independent; two

b. Dependent; two

c. Independent; multiple

d. Dependent; Multiple

**16. If we want to estimate the average height of students in an elementary school, which of the following situations can certainly cause bias in our estimation?**

a. If the rulers we use systematically overestimate the students’ heights

b. If we only sample the female students in that elementary school

c. If we use random sampling method to select students

d. If we only selected students who were eager to participate in the study

**17. The sampling variability of a statistic refers to how much the statistic varies from sample to sample and is usually measured by its:**

a. standard error

b. standard deviation

c. average

d. median

**18. A graduate school Professor wanted to know average age of students in his class. He randomly selected five students and obtained their ages. Their ages were 26, 32, 22, 21, and 25 years. What’s the standard error of the mean from our sample estimation? **

**19. Which of the assumption is NOT required to compute a confidence interval for the difference between two means? **

a. The two populations have the same variance.

b. The populations are normally distributed.

c. Each value is sampled independently from each other value.

d. The two populations have the similar means.

**20. For a t distribution with 1,000 degrees of freedom, 99% of the distribution is within how many standard deviations of the mean? **

a. One

b. Two

c. Three

d. Four

**1.**

**6.**

**11.**

**16.**

**2.**

**7.**

**12.**

**17.**

**3.**

**8.**

**13.**

**18.**

**4.**

**9.**

**14.**

**19.**

**5.**

**10.**

**15.**

**20.**

**CALCULATIONS (SHOW PROBLEM NUMBER)**