Question 1

A pharmaceutical company wants to summarize the ages of participants in a clinical trial. Which of the following is NOT a proper method for presenting this quantitative data?

Accepted Answer

Using a bar graph to display the mean age

Question 2

Which of the following formulas correctly calculates the sample variance $$s^2$$ for a data set with $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$ and sample mean $$\bar{x}$$?

Accepted Answer

$$s^2$$ = \frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x}$$)^2$$

Question 3

A hospital administrator wants to estimate the average length of stay for patients. She takes a random sample of 100 patients and finds a sample mean of 4.2 days with a standard deviation of 1.5 days. What is the 95% confidence interval for the population mean length of stay? (Use $$z^* = 1.96)$$

Accepted Answer

$$4.2 \pm 0.294$$

Question 4

Which of the following statements about the Central Limit Theorem (CLT) is TRUE?

Accepted Answer

The CLT states that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the population's distribution.

Question 5

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 p = 0.5$)

Accepted Answer

$$P(X=6) = \binom{10}{6} (0.5)^6$ (0.5)^4$

Question 6

A researcher wants to test if a new drug changes blood pressure. The null hypothesis is $$H_0$$: \mu = 120$$ mmHg. The sample mean is 123 mmHg, sample standard deviation is 8 mmHg, and sample size is 25. What is the value of the test statistic?

Accepted Answer

$$z = \frac{123 - 120}{8/\sqrt{25}} = 1.875$$

Question 7

Which of the following is an example of a Type I error in hypothesis testing?

Accepted Answer

Rejecting the null hypothesis when it is actually true

Question 8

A study finds a correlation coefficient $$r = 0.85$$ between hours studied and exam scores. Which of the following best describes this relationship?

Accepted Answer

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

Question 9

Which of the following is the correct formula for the regression line predicting $$y$$ from $$x$$?

Accepted Answer

$$\hat{y} = b_0$ + b_1$ x$$

Question 10

A quality control manager wants to test if the proportion of defective products is different from 5%. Which hypothesis test should be used?

Accepted Answer

One-sample proportion $$z-$$test

Question 11

A researcher collects data on blood type (A, B, AB, O) and gender (male, female) for a group of patients. Which statistical test is most appropriate to determine if blood type and gender are independent?

Accepted Answer

Chi-square test of independence

Question 12

Which of the following is NOT an assumption of the standard normal distribution?

Accepted Answer

The mean is 1

Question 13

A company wants to compare the mean salaries of employees in three different departments. Which statistical method should be used?

Accepted Answer

Analysis of variance (ANOVA)

Question 14

If the probability of rain on any given day is 0.3, what is the probability that it will rain on exactly 2 out of 5 days? (Use the binomial formula)

Accepted Answer

$$P(X=2) = \binom{5}{2} (0.3)^2$ (0.7)^3$

Question 15

Which of the following best describes the purpose of constructing a confidence interval?

Accepted Answer

To estimate a population parameter with an associated level of certainty

Question 16

A researcher wants to know if a new teaching method affects test scores. She randomly assigns students to two groups: one uses the new method, the other uses the traditional method. Which test should she use to compare the means of the two groups?

Accepted Answer

Two-sample $$t-$$test

Question 17

Which of the following is the correct formula for the probability of the complement of event $$A$$?

Accepted Answer

$$P(A^c) = 1 - P(A)$$

Question 18

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 $$z-$$score for a person with a cholesterol level of 240 mg/dL?

Accepted Answer

$$z = \frac{240 - 200}{20} = 2$$

Question 19

Which of the following is a correct interpretation of a $$p-$$value in hypothesis testing?

Accepted Answer

The probability of observing a test statistic as extreme as, or more extreme than, the observed value, assuming the null hypothesis is true

Question 20

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

Accepted Answer

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

Elementary Statistics: Course Overview and Key Concepts

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