Q: A sample of 100 patients has a mean cholesterol level of 200 mg/dL with a standard deviation of 20 mg/dL. What is the 95% confidence interval for the population mean cholesterol level? (Use $$z^* = 1.96)$$

$$200 \pm 1.96 \times \frac{20}{\sqrt{100}} = 200 \pm 3.92$$

Question 1

Which of the following best describes the difference between descriptive and inferential statistics?

Accepted Answer

Descriptive statistics summarize and organize data, while inferential statistics use data from a sample to make conclusions about a population.

Question 2

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 type of statistical study they should use?

Accepted Answer

A randomized controlled experiment, where participants are randomly assigned to receive either the new drug or the standard treatment.

Question 3

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

Accepted Answer

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

Question 4

A researcher collects data on the number of hours students study per week and their final exam scores. Which statistical method is most appropriate to explore the relationship between these two variables?

Accepted Answer

Simple linear regression and correlation analysis.

Question 5

Suppose the heights of adult men in a city are normally distributed with mean $$\mu = 70$$ inches and standard deviation $$\sigma = 3$$ inches. What is the $$z-$$score for a man who is 76 inches tall?

Accepted Answer

$$z = \frac{76 - 70}{3} = 2$$

Question 6

Which of the following is a key ethical consideration when conducting a statistical study involving human subjects?

Accepted Answer

Obtaining informed consent from all participants.

Question 7

A fair six-sided die is rolled. What is the probability of rolling a number greater than 4?

Accepted Answer

$$P = \frac{2}{6} = \frac{1}{3}$$

Question 8

Which of the following best describes a confidence interval?

Accepted Answer

A range of values, derived from sample statistics, that is likely to contain the population parameter with a specified level of confidence.

Question 9

A sample of 100 patients has a mean cholesterol level of 200 mg/dL with a standard deviation of 20 mg/dL. What is the 95% confidence interval for the population mean cholesterol level? (Use $$z^* = 1.96)$$

Accepted Answer

$$200 \pm 1.96 	imes \frac{20}{\sqrt{100}} = 200 \pm 3.92$$

Question 10

Which of the following statements about hypothesis testing is correct?

Accepted Answer

The null hypothesis is rejected if the $$p-$$value is less than the significance level $$\alpha.$$

Question 11

A researcher wants to estimate the proportion of voters in a city who support a new policy. Which sampling method would provide the most reliable results?

Accepted Answer

Simple random sampling of registered voters.

Question 12

If the correlation coefficient $$r$$ between two variables is $$-0.85$$, what does this indicate?

Accepted Answer

There is a strong negative linear relationship between the two variables.

Question 13

Which of the following is the correct formula for the variance $$s^2 of a $$sample of $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$ with mean $$\bar{x}$$?

Accepted Answer

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

Question 14

A hospital administrator wants to know if a new scheduling system reduces patient wait times. She collects wait time data before and after implementation. Which hypothesis test is most appropriate?

Accepted Answer

A paired $$t-$$test comparing mean wait times before and after.

Question 15

Which of the following is an example of a categorical (qualitative) variable?

Accepted Answer

Blood type (A, B, AB, O)

Question 16

A study finds that the average test score in a class is 75 with a standard deviation of 10. If the scores are approximately normally distributed, what percentage of students scored between 65 and 85?

Accepted Answer

About 68%, since 65 and 85 are one standard deviation below and above the mean.

Question 17

Which of the following is a potential source of bias in a statistical study?

Accepted Answer

Using a non-random sample that does not represent the population.

Question 18

A researcher is interested in the relationship between hours of sleep and reaction time. She finds a correlation coefficient of $$r = 0.05. $$What does this suggest?

Accepted Answer

There is little to no linear relationship between hours of sleep and reaction time.

Question 19

Which of the following best describes the purpose of using a sampling distribution in inferential statistics?

Accepted Answer

To understand the variability of a statistic from sample to sample and to make inferences about the population parameter.

Question 20

A student calculates a $$p-$$value of 0.03 when testing $$H_0$$: \mu = 100$$ against H_a$$: \mu 
eq 100$$ at $$\alpha = 0.05$$. What is the correct conclusion?

Accepted Answer

Reject the null hypothesis; there is significant evidence that $$\mu 
eq 100.$$

Elementary Statistics (STATB201) Syllabus and Course Structure Study Notes

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