Q: A bag contains 5 red balls and 7 blue balls. If two balls are drawn one after another with replacement, what is the probability both are red?

$$\frac{5}{12} \times \frac{5}{12}$$

Question 1

A researcher compares the mean cholesterol levels of two independent groups: one taking a new medication and one taking a placebo. The 95% confidence interval for the difference in means is $$[2.1, 8.7]. $$What does this confidence interval suggest?

Accepted Answer

The mean cholesterol level for the medication group is significantly higher than the placebo group by between 2.1 and 8.7 units.

Question 2

Which of the following is NOT part of the 5-number summary for a data set?

Accepted Answer

Mean

Question 3

Given the data set: $$2, 4, 7, 10, 15$$, what is the median?

Accepted Answer

$$7$$

Question 4

Which of the following best defines a Type II error in hypothesis testing?

Accepted Answer

Failing to reject the null hypothesis when it is false.

Question 5

A sample of home prices contains several extremely high values. Which measure of central tendency is most affected by these outliers?

Accepted Answer

Mean

Question 6

Suppose you roll a fair six-sided die. What is the empirical probability of rolling a number greater than 4 after 60 rolls, if you observed 22 such outcomes?

Accepted Answer

$$\frac{22}{60}$$

Question 7

Which of the following is the correct symbolic form for the null and alternative hypotheses for testing if the mean weight of apples is less than 150g?

Accepted Answer

$$H_0$$: \mu \geq 150$$, H_1$: \mu \u003c 150$$

Question 8

A data value is 2 standard deviations above the mean. What is its $$z-$$score?

Accepted Answer

$$z = 2$$

Question 9

Which of the following statements about the correlation coefficient $$r is $$TRUE?

Accepted Answer

$$r$$ measures the strength and direction of a linear relationship between two variables.

Question 10

A grouped frequency distribution has class limits 10-19, 20-29, 30-39, 40-49. What is the class width?

Accepted Answer

$$10$$

Question 11

Which of the following is a parameter?

Accepted Answer

The mean height of all students in a university.

Question 12

A study wants to estimate the average commute time for all workers in a city. Which sampling method is used if the city is divided into neighborhoods and a random sample of neighborhoods is selected, then all workers in those neighborhoods are surveyed?

Accepted Answer

Cluster sampling

Question 13

If the variance of a data set is $$16$$, what is the standard deviation?

Accepted Answer

$$4$$

Question 14

Which of the following is a discrete random variable?

Accepted Answer

The number of cars passing through a toll booth in an hour.

Question 15

A bag contains 5 red balls and 7 blue balls. If two balls are drawn one after another with replacement, what is the probability both are red?

Accepted Answer

$$\frac{5}{12} 	imes \frac{5}{12}$$

Question 16

Which of the following is the correct formula for the margin of error $$E$$ for a confidence interval for a population mean when the population standard deviation $$\sigma is $$known?

Accepted Answer

$$E = z_{\alpha/2} \cdot \frac{\sigma}{\sqrt{n}}$$

Question 17

A researcher wants to test if a new teaching method improves test scores. Which type of hypothesis test should be conducted?

Accepted Answer

A two-sample $$t-$$test for means

Question 18

Which of the following is TRUE about mutually exclusive events?

Accepted Answer

They cannot occur at the same time.

Question 19

A point at coordinates $$(8, 2) on a $$scatterplot is far from the regression line and influences the slope significantly. This point is:

Accepted Answer

An influential point

Question 20

A 95% confidence interval for the mean is $$(12.5, 17.5). $$What is the margin of error $$E$$?

Accepted Answer

$$E = \frac{17.5 - 12.5}{2} = 2.5$$

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