Q: A pharmaceutical company tests a new drug on 100 patients and finds that 60% show improvement. What is the 95% confidence interval for the proportion of patients who improve? (Use $$ z = 1.96 $$ for 95% confidence)

$$ 0.60 \pm 1.96 \times \sqrt{\frac{0.60 \times 0.40}{100}} $$

Question 1

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

Accepted Answer

A population includes all elements of interest, while a sample is a subset selected from the population.

Question 2

A researcher wants to study the average height of adult males in a city. Which scale of measurement is most appropriate for height?

Accepted Answer

Ratio

Question 3

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

Accepted Answer

Variance

Question 4

Given the following data set: 2, 4, 6, 8, 10. What is the variance of the data set?

Accepted Answer

$$ 10 $$

Question 5

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

Accepted Answer

It states that as sample size increases, the distribution of sample means approaches a normal distribution, regardless of the population's distribution.

Question 6

A pharmaceutical company tests a new drug on 100 patients and finds that 60% show improvement. What is the 95% confidence interval for the proportion of patients who improve? (Use $$ z = 1.96 $$ for 95% confidence)

Accepted Answer

$$ 0.60 \pm 1.96 	imes \sqrt{\frac{0.60 	imes 0.40}{100}} $$

Question 7

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

Accepted Answer

Rejecting a true null hypothesis.

Question 8

A teacher wants to compare the average test scores of two classes. Which statistical test is most appropriate?

Accepted Answer

Two-sample t-test

Question 9

If the p-value in a hypothesis test is 0.03 and the significance level $$ \alpha  is 0.05$$, what should the researcher conclude?

Accepted Answer

Reject the null hypothesis.

Question 10

Which of the following is a disadvantage of using convenience sampling?

Accepted Answer

It may not be representative of the population.

Question 11

A psychologist measures the stress levels of participants before and after a meditation session. Which statistical technique should be used to analyze the difference?

Accepted Answer

Paired t-test

Question 12

Which formula is used to calculate the mean of a discrete probability distribution?

Accepted Answer

$$ \mu = \sum x \cdot P(x) $$

Question 13

A business analyst uses linear regression to predict sales based on advertising spending. Which statistic measures the strength and direction of the linear relationship?

Accepted Answer

Correlation coefficient ($$ r )$$

Question 14

Which of the following is true about the normal distribution?

Accepted Answer

It has mean, median, and mode all equal.

Question 15

A social scientist wants to test whether the proportion of voters supporting a candidate is different from 0.5. Which hypothesis test should be used?

Accepted Answer

One-sample proportion z-test

Question 16

Which formula is used to calculate the variance of a discrete probability distribution?

Accepted Answer

$$ \$$sigma^2$$ = \sum (x - \mu)^2$ \cdot P(x) $$

Question 17

A medical researcher wants to estimate the average blood pressure in a population. Which sampling method would best minimize bias?

Accepted Answer

Random sampling

Question 18

Which of the following is an example of an interval scale?

Accepted Answer

Temperature in Celsius

Question 19

If a data set is displayed in a histogram and shows a long tail to the right, how is the distribution described?

Accepted Answer

Skewed right

Question 20

A researcher uses technology to analyze data and obtains a regression output with $$ R^2$ = 0.85 . $$What does this value indicate?

Accepted Answer

85% of the variation in the dependent variable is explained by the model.

Introductory Statistics: Course Syllabus and Key Learning Outcomes

Guida di studio - Domande di pratica

Study guide - Flashcard