Question 1

A pharmaceutical company wants to test whether a new drug lowers blood pressure more effectively than the current standard. Which of the following best describes the null hypothesis ($$H_0) $$for this study?

Accepted Answer

$$H_0$$: There is no difference in blood pressure reduction between the new drug and the current standard.

Question 2

Which of the following is the correct formula for the sample mean $$\bar{x} of a $$dataset with $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

$$\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$$

Question 3

A researcher collects the heights of 100 college students. Which measure of central tendency is most appropriate if the data are normally distributed?

Accepted Answer

Mean

Question 4

Which of the following is the correct formula for the standard deviation $$s of a $$sample?

Accepted Answer

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

Question 5

A hospital administrator wants to estimate the average length of stay for patients. Which type of sampling would best ensure that all departments are represented proportionally?

Accepted Answer

Stratified sampling

Question 6

If the probability of a patient recovering from a surgery is $$0.8$$, what is the probability that two independent patients both recover?

Accepted Answer

$$0.8 	imes 0.8 = 0.64$$

Question 7

A study finds that the correlation coefficient between hours studied and exam score is $$r = 0.85. $$What does this indicate?

Accepted Answer

There is a strong positive linear relationship.

Question 8

Which of the following is the correct formula for the binomial probability of getting exactly $$k$$ successes in $$n$$ independent trials, each with probability $$p of $$success?

Accepted Answer

$$P(X = k) = \binom{n}{k} p^k (1-p$$)^{n-k}$$

Question 9

A medical test for a rare disease has a sensitivity of $$95\%$$ and a specificity of $$90\%. If a $$patient tests positive, which statistical concept helps determine the probability that the patient actually has the disease?

Accepted Answer

Bayes' Theorem

Question 10

A sample of 50 students has a mean test score of 75 and a standard deviation of 10. What is the $$z-$$score for a student who scored 85?

Accepted Answer

$$z = \frac{85 - 75}{10} = 2$$

Question 11

Which of the following statements about the Central Limit Theorem is correct?

Accepted Answer

It states that the distribution of sample means approaches a normal distribution as sample size increases.

Question 12

A researcher wants to test if a coin is fair. She flips it 100 times and gets 60 heads. Which statistical test is most appropriate?

Accepted Answer

One-sample $$z-$$test for proportions

Question 13

Which formula correctly calculates the confidence interval for a population mean when the population standard deviation is unknown?

Accepted Answer

$$\bar{x} \pm t^* \frac{s}{\sqrt{n}}$$

Question 14

A factory produces light bulbs with a mean lifetime of 1200 hours and a standard deviation of 100 hours. What percentage of bulbs are expected to last between 1100 and 1300 hours, assuming a normal distribution?

Accepted Answer

About 68\%

Question 15

Which of the following is NOT an assumption of the one-sample $$t-$$test?

Accepted Answer

The population standard deviation is known.

Question 16

A study finds that the mean cholesterol level in a sample of adults is 200 mg/dL with a standard deviation of 20 mg/dL. If the sample size is 25, what is the standard error of the mean?

Accepted Answer

$$\frac{20}{\sqrt{25}} = 4$$

Question 17

Which of the following best describes a Type I error in hypothesis testing?

Accepted Answer

Rejecting a true null hypothesis.

Question 18

A researcher wants to compare the mean test scores of three different teaching methods. Which statistical test should be used?

Accepted Answer

ANOVA (Analysis of Variance)

Question 19

Which formula is used to calculate the expected value $$E(X) of a $$discrete random variable $$X$$ with possible values $$x_1$$, $$x_2$$, ..., x_n$$ and probabilities p_1$, p_2$, ..., p_n$$?

Accepted Answer

$$E(X) = \sum_{i=1}^{n} x_i p_i$$

Statistics Syllabus and Study Guide: Key Concepts, Course Structure, and Academic Expectations

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