Q: A pharmaceutical company wants to estimate the average recovery time for a new drug. They collect a random sample of 50 patients and find a sample mean recovery time of 8 days with a sample standard deviation of 2 days. What is the 95% confidence interval for the population mean recovery time? (Assume normality.)

The confidence interval is $$8 \pm 1.96 \times \frac{2}{\sqrt{50}}$$, which is $$(7.45, 8.55).$$

Q: A business analyst uses regression analysis to predict sales based on advertising spending. The regression equation is $$y = 500 + 20x$$, where $$y is $$sales and $$x is $$advertising spending in thousands of dollars. What is the predicted sales if advertising spending is $10,000?

Predicted sales is $$y = 500 + 20 \times 10 = 700$$

Question 1

Which of the following best describes the Central Limit Theorem (CLT) and its significance in inferential statistics?

Accepted Answer

The CLT states that as sample size increases, the sampling distribution of the sample mean approaches a normal distribution, regardless of the population's distribution.

Question 2

A pharmaceutical company wants to estimate the average recovery time for a new drug. They collect a random sample of 50 patients and find a sample mean recovery time of 8 days with a sample standard deviation of 2 days. What is the 95% confidence interval for the population mean recovery time? (Assume normality.)

Accepted Answer

The confidence interval is $$8 \pm 1.96 	imes \frac{2}{\sqrt{50}}$$, which is $$(7.45, 8.55).$$

Question 3

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

Accepted Answer

Standard deviation

Question 4

A researcher is testing whether a new teaching method improves test scores. The null hypothesis is $$H_0$$: \mu = 75$$ and the alternative is H_a$$: \mu \u003e 75$$. If the p-value is 0.03 and the significance level is 0.05, what should the researcher conclude?

Accepted Answer

Reject the null hypothesis; there is significant evidence that the new method improves scores.

Question 5

Which of the following statements about Type I and Type II errors is correct?

Accepted Answer

Type I error occurs when you reject a true null hypothesis.

Question 6

A hospital administrator wants to know if there is a relationship between patient satisfaction (high/low) and department (ER, Surgery, Pediatrics). Which statistical test should be used?

Accepted Answer

Chi-square test for independence

Question 7

In a binomial distribution, which formula gives the probability of exactly $$k$$ successes in $$n$$ trials, with probability $$p of $$success on each trial?

Accepted Answer

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

Question 8

A social scientist collects data on income and education level for 200 individuals. She calculates the correlation coefficient $$r = 0.65. $$What does this value indicate?

Accepted Answer

There is a strong positive linear relationship between income and education level.

Question 9

Which of the following is an example of a discrete probability distribution?

Accepted Answer

Binomial distribution

Question 10

A psychologist wants to compare the mean anxiety scores of two groups: those who received therapy and those who did not. Which statistical test is most appropriate?

Accepted Answer

Two-sample t-test

Question 11

Which formula is used to calculate the sample variance $$s^2$$ for a set of $$n$$ data points $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

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

Question 12

A business analyst uses regression analysis to predict sales based on advertising spending. The regression equation is $$y = 500 + 20x$$, where $$y is $$sales and $$x is $$advertising spending in thousands of dollars. What is the predicted sales if advertising spending is $10,000?

Accepted Answer

Predicted sales is $$y = 500 + 20 	imes 10 = 700$$

Question 13

Which of the following is a correct interpretation of a 95% confidence interval for a population mean?

Accepted Answer

We are 95% confident that the interval contains the true population mean.

Question 14

A researcher wants to test if three different diets result in different average weight loss. Which statistical method should be used?

Accepted Answer

ANOVA (Analysis of Variance)

Question 15

Which formula is used to calculate the z-score for a value $$x in a $$population with mean $$\mu$$ and standard deviation $$\sigma$$?

Accepted Answer

$$z = \frac{x - \mu}{\sigma} $$

Question 16

Which of the following is an example of a real-world application of hypothesis testing?

Accepted Answer

Determining if a new medication lowers blood pressure more than the current standard treatment.

Question 17

A school administrator wants to estimate the proportion of students who prefer online classes. In a random sample of 200 students, 120 prefer online classes. What is the point estimate for the proportion?

Accepted Answer

$$\hat{p} = \frac{120}{200} = 0.6 $$

Question 18

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

Accepted Answer

It may not be representative of the population, leading to biased results.

Question 19

A health scientist wants to test if the proportion of smokers differs between two cities. Which statistical test should be used?

Accepted Answer

Two-proportion z-test

Question 20

Which formula is used to calculate the regression line (least squares) for predicting $$y$$ from $$x$$?

Accepted Answer

$$y = a + bx $$

Introductory Statistics Course Syllabus and Learning Outcomes

Guida di studio - Domande di pratica

Study guide - Flashcard