Question 1

A pharmaceutical company wants to compare the effectiveness of two drugs. They collect data from two independent samples of patients, one for each drug. Which statistical method is most appropriate to determine if there is a significant difference in the mean effectiveness between the two drugs?

Accepted Answer

Two-sample t-test

Question 2

A researcher records the following data set of exam scores: 70, 75, 80, 85, 90. What is the standard deviation of this data set? (Round to the nearest whole number.)

Accepted Answer

$$7$$

Question 3

A fair coin is flipped 10 times. What is the probability of getting exactly 6 heads? (Use the binomial formula: $$P(X = k) = \binom{n}{k} p^k (1-p$$)^{n-k}$$, where n=10$, k=6$, p=0.5$)

Accepted Answer

$$P = 0.205$$

Question 4

A hospital administrator wants to know if the distribution of blood types among patients matches the national distribution. Which statistical test should be used?

Accepted Answer

Chi-square goodness-of-fit test

Question 5

A data set has a mean of 50 and a standard deviation of 5. What is the z-score for a value of 60?

Accepted Answer

$$z = 2$$

Question 6

A sample of 100 students has a mean test score of 75 with a standard deviation of 10. Construct a 95% confidence interval for the population mean. (Use $$z^* = 1.96$$ for 95% confidence.)

Accepted Answer

$$[73.04, 76.96]$$

Question 7

Which of the following is NOT a measure of central tendency?

Accepted Answer

Standard deviation

Question 8

A researcher finds a correlation coefficient $$r = 0.85$$ between hours studied and exam scores. What does this indicate?

Accepted Answer

There is a strong positive linear relationship between hours studied and exam scores.

Question 9

A normal distribution has a mean of 100 and a standard deviation of 15. What percentage of data falls between 85 and 115?

Accepted Answer

About 68%

Question 10

A teacher wants to know if a new teaching method improves test scores. She tests the same group of students before and after using the new method. Which hypothesis test should she use?

Accepted Answer

Paired t-test

Question 11

Which graphical representation is most appropriate for displaying the distribution of a single quantitative variable?

Accepted Answer

Histogram

Question 12

If the probability of rain tomorrow is 0.3, what is the probability that it will not rain?

Accepted Answer

$$0.7$$

Question 13

A researcher wants to estimate the proportion of voters who support a new policy. In a random sample of 400 voters, 220 support the policy. What is the sample proportion?

Accepted Answer

$$0.55$$

Question 14

Which of the following statements about the binomial distribution is TRUE?

Accepted Answer

The number of trials is fixed.

Question 15

A study finds that the mean cholesterol level in a population is 200 mg/dL with a standard deviation of 20 mg/dL. What is the percentile rank of a person with a cholesterol level of 220 mg/dL? (Assume normal distribution.)

Accepted Answer

About the 84th percentile

Question 16

Which of the following is an example of inferential statistics?

Accepted Answer

Using a sample to estimate the average height of all adults in a city

Question 17

A researcher wants to test if there is an association between gender (male/female) and preference for a new product (like/dislike). Which statistical test should be used?

Accepted Answer

Chi-square test for independence

Question 18

If a data set is skewed to the right, which measure of central tendency is likely to be the largest?

Accepted Answer

Mean

Question 19

A scientist collects data on the number of bacteria colonies in petri dishes after applying a new disinfectant. Which type of variable is being measured?

Accepted Answer

Quantitative discrete

Question 20

A researcher wants to use the normal distribution to approximate a binomial distribution. Which condition must be met?

Accepted Answer

$$np \geq 5$$ and $$n(1-p) \geq 5$$

MATH 200 - Statistics: Course Outline and Key Concepts

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