Q: A sample of 50 patients has a mean systolic blood pressure of 130 mmHg and a standard deviation of 10 mmHg. What is the 95% confidence interval for the mean? (Use $$z = 2$$ for simplicity.)

$$130 \pm 2 \times \frac{10}{\sqrt{50}}$$

Question 1

Which of the following best describes the difference between a parameter and a statistic?

Accepted Answer

A parameter is a numerical summary of a population, while a statistic is a numerical summary of a sample.

Question 2

A pharmaceutical company wants to test if a new drug lowers blood pressure more effectively than the current standard. Which hypothesis test should they use if they collect data from two independent groups?

Accepted Answer

A two-sample t-test

Question 3

Suppose a researcher collects the following data: $$2, 4, 4, 6, 8. $$What is the mean of this data set?

Accepted Answer

$$\frac{2+4+4+6+8}{5} = 4.8$$

Question 4

Which of the following is NOT an assumption for conducting a one-sample t-test?

Accepted Answer

The population standard deviation is known.

Question 5

A 95% confidence interval for the mean cholesterol level in a population is $$(180, 200). $$Which interpretation is correct?

Accepted Answer

We are 95% confident that the population mean is between 180 and 200.

Question 6

If the null hypothesis is true, what is the probability of making a Type I error?

Accepted Answer

$$\alpha$$

Question 7

Which of the following best describes the Central Limit Theorem?

Accepted Answer

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

Question 8

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 9

Which formula is used to calculate the standard error of the mean for a sample of size $$n$$ with standard deviation $$s$$?

Accepted Answer

$$\frac{s}{\sqrt{n}}$$

Question 10

A researcher wants to estimate the proportion of voters who support a new policy. Which distribution should be used to model the number of supporters in a random sample of 100 voters?

Accepted Answer

Binomial distribution

Question 11

Which of the following is a correct interpretation of a p-value?

Accepted Answer

The probability of obtaining a result as extreme as, or more extreme than, the observed result, assuming the null hypothesis is true.

Question 12

A sample of 50 patients has a mean systolic blood pressure of 130 mmHg and a standard deviation of 10 mmHg. What is the 95% confidence interval for the mean? (Use $$z = 2$$ for simplicity.)

Accepted Answer

$$130 \pm 2 	imes \frac{10}{\sqrt{50}}$$

Question 13

Which of the following is an example of a categorical variable?

Accepted Answer

Blood type (A, B, AB, O)

Question 14

If a 90% confidence interval for a mean is $$(50, 60)$$, what will happen to the width of the interval if the confidence level is increased to 99%?

Accepted Answer

The interval will become wider.

Question 15

A hospital administrator wants to know if the average length of stay for patients has changed from last year’s average of 5 days. Which hypothesis test should be used?

Accepted Answer

A one-sample t-test

Question 16

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

Accepted Answer

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

Question 17

A researcher is interested in the relationship between exercise frequency (measured in days per week) and cholesterol level. Which statistical method is most appropriate?

Accepted Answer

Linear regression

Question 18

Which of the following statements about the null hypothesis $$H_0 is $$true?

Accepted Answer

It is rejected if the p-value is less than $$\alpha.$$

Question 19

A fair coin is flipped 10 times. What is the probability of getting exactly 5 heads? (Use the binomial formula: $$P(X = k) = \binom{n}{k} p^k (1-p$$)^{n-k}$$, with p = 0.5$)

Accepted Answer

$$\binom{10}{5} (0.5)^5$ (0.5)^5$

Question 20

Which of the following is a correct statement about Type II error?

Accepted Answer

It occurs when the null hypothesis is false but not rejected.

MATH 158: Introductory Data Analysis Syllabus – Key Topics and Structure

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