Q: A pharmaceutical company tests a new drug on a sample of 100 patients and finds a mean reduction in blood pressure of $$8$$ mmHg with a standard deviation of $$2$$ mmHg. What is the $$95\%$$ confidence interval for the mean reduction in blood pressure? (Assume normality)

$$8 \pm 1.96 \times \dfrac{2}{\sqrt{100}}$$

Q: If the probability of a patient recovering from a disease is $$0.7$$, what is the probability that exactly 2 out of 3 patients recover? (Assume independence)

$$3 \times (0.7)^2$ \times (0.3)$$

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 sample data to make generalizations about a population.

Question 2

A researcher wants to compare the average test scores of students from two different schools. Which scale of measurement is most appropriate for the test scores?

Accepted Answer

Interval

Question 3

Which sampling method is most likely to introduce bias if used to select participants for a medical study?

Accepted Answer

Convenience sampling

Question 4

Given the following data set representing the number of books read by 8 students in a month: 2, 4, 4, 5, 6, 7, 8, 10. What is the median number of books read?

Accepted Answer

$$5.5$$

Question 5

A pharmaceutical company tests a new drug on a sample of 100 patients and finds a mean reduction in blood pressure of $$8$$ mmHg with a standard deviation of $$2$$ mmHg. What is the $$95\%$$ confidence interval for the mean reduction in blood pressure? (Assume normality)

Accepted Answer

$$8 \pm 1.96 	imes \dfrac{2}{\sqrt{100}}$$

Question 6

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, regardless of the population's distribution.

Question 7

A hospital administrator wants to test whether the average length of stay for patients has changed from the historical mean of $$5$$ days. Which is the appropriate null hypothesis for this test?

Accepted Answer

$$H_0$$: \mu = 5$$

Question 8

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

Accepted Answer

Rejecting a true null hypothesis

Question 9

A study finds a correlation coefficient $$r = 0.85$$ between hours studied and exam scores. What does this indicate?

Accepted Answer

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

Question 10

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

Accepted Answer

$$s = \sqrt{\dfrac{\sum (x_i - \bar{x})^2$}{n-1}}$$

Question 11

A researcher is analyzing categorical data on favorite ice cream flavors. Which statistical test is most appropriate to determine if there is a significant difference in preferences among three flavors?

Accepted Answer

Chi-square test

Question 12

In a normal distribution, what percentage of data falls within two standard deviations of the mean?

Accepted Answer

$$95\%$$

Question 13

A company wants to estimate the proportion of defective products in a large shipment. Which formula should be used to calculate the standard error of the sample proportion $$\hat{p}$$?

Accepted Answer

$$SE = \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$$

Question 14

Which of the following is NOT a measure of central tendency?

Accepted Answer

Range

Question 15

A biologist collects data on the heights of plants and wants to compare the variability of two different species. Which measure should be used?

Accepted Answer

Standard deviation

Question 16

A psychologist wants to test if there is a difference in mean anxiety scores among three different therapy groups. Which statistical method should be used?

Accepted Answer

One-way ANOVA

Question 17

If the probability of a patient recovering from a disease is $$0.7$$, what is the probability that exactly 2 out of 3 patients recover? (Assume independence)

Accepted Answer

$$3 	imes (0.7)^2$ 	imes (0.3)$$

Question 18

Which of the following best describes a continuous random variable?

Accepted Answer

It can take on any value within a given range.

Question 19

A teacher wants to know if students who use a new study app score higher than those who do not. Which statistical test should be used to compare the means of the two independent groups?

Accepted Answer

Independent samples t-test

Question 20

Which of the following is the correct formula for the linear regression line?

Accepted Answer

$$y = a + bx$$

STATC1000: Introduction to Statistics – Syllabus and Core Concepts Study Guide

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