Q: A researcher wants to estimate the average number of hours college students sleep per night. She randomly selects 100 students and finds a sample mean of 6.8 hours with a standard deviation of 1.2 hours. What is the 95% confidence interval for the mean? (Use $$z^* = 1.96)$$

$$6.8 \pm 1.96 \times \dfrac{1.2}{\sqrt{100}}$$

Question 1

Which of the following best describes the primary purpose of using descriptive statistics in a medical research study investigating the average recovery time after a new surgical procedure?

Accepted Answer

To summarize and present the main features of the collected recovery time data using measures such as mean, median, and standard deviation.

Question 2

A pharmaceutical company wants to test whether a new drug lowers blood pressure more effectively than the current standard. Which statistical method should they use to determine if the observed difference in mean blood pressure reduction is statistically significant?

Accepted Answer

Inferential statistics, such as hypothesis testing

Question 3

Suppose a dataset of exam scores is highly skewed to the right. Which measure of central tendency would be most appropriate to report as a summary of the typical score?

Accepted Answer

The median, because it is less affected by extreme values.

Question 4

A hospital administrator wants to compare the average length of stay for patients in two different departments. Which statistical technique is most appropriate for this comparison?

Accepted Answer

Performing a two-sample t-test

Question 5

If the probability of a patient experiencing a side effect from a medication is $$0.15$$, what is the probability that out of 10 patients, exactly 2 will experience the side effect? (Assume independence.)

Accepted Answer

$$P = \binom{10}{2} (0.15)^2$ (0.85)^8$

Question 6

A researcher collects data on the number of hours students study per week and their final exam scores. Which statistical method would best model the relationship between these two quantitative variables?

Accepted Answer

Linear regression analysis

Question 7

Which of the following statements about confidence intervals is TRUE?

Accepted Answer

A 95% confidence interval means that if we repeated the sampling process many times, about 95% of the calculated intervals would contain the true population parameter.

Question 8

A study finds a correlation coefficient $$r = 0.85$$ between hours of exercise per week and HDL cholesterol levels. Which of the following best describes this relationship?

Accepted Answer

There is a strong positive linear relationship between hours of exercise and HDL cholesterol.

Question 9

A clinical trial tests whether a new vaccine is effective. The null hypothesis is that the vaccine has no effect. The p-value is found to be $$0.03. $$What is the correct interpretation if the significance level is $$\alpha = 0.05$$?

Accepted Answer

Reject the null hypothesis; there is statistically significant evidence that the vaccine is effective.

Question 10

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

Accepted Answer

The blood type of a patient (A, B, AB, O)

Question 11

A researcher wants to estimate the average number of hours college students sleep per night. She randomly selects 100 students and finds a sample mean of 6.8 hours with a standard deviation of 1.2 hours. What is the 95% confidence interval for the mean? (Use $$z^* = 1.96)$$

Accepted Answer

$$6.8 \pm 1.96 	imes \dfrac{1.2}{\sqrt{100}}$$

Question 12

Which of the following best describes the difference between a population and a sample in statistics?

Accepted Answer

A sample is a subset of the population used to make inferences about the population.

Question 13

A teacher wants to know if a new teaching method improves test scores. She randomly assigns students to two groups: one uses the new method, the other uses the traditional method. Which type of study design is this?

Accepted Answer

Experimental study

Question 14

If the standard deviation of a dataset is zero, what can you conclude about the data?

Accepted Answer

All data values are the same.

Question 15

A city health department wants to know if there is an association between smoking status (smoker/non-smoker) and the presence of lung disease (yes/no). Which statistical test is most appropriate?

Accepted Answer

Chi-square test for independence

Question 16

A researcher finds that the regression equation for predicting weight (in kg) from height (in cm) is $$	ext{Weight} = 0.5 	imes 	ext{Height} - 30. $$What is the predicted weight for a person who is 170 cm tall?

Accepted Answer

$$0.5 	imes 170 - 30 = 55 kg$$

Question 17

Which of the following is NOT an assumption of simple linear regression?

Accepted Answer

The dependent variable must be categorical.

Question 18

A study reports a p-value of $$0.08$$ for the effect of a new diet on cholesterol levels. If the significance level is $$\alpha = 0.05$$, what should the researchers conclude?

Accepted Answer

Fail to reject the null hypothesis; there is not enough evidence to conclude the diet has an effect.

Question 19

Which of the following best describes the main goal of inferential statistics?

Accepted Answer

To make predictions or draw conclusions about a population based on sample data.

STA 2023: Introductory Statistics – Syllabus and Course Structure Study Notes

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