Question 1

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

Accepted Answer

A population includes all members of a defined group, while a sample is a subset selected from that population.

Question 2

A researcher wants to estimate the average cholesterol level of adults in a city. She randomly selects 200 adults and measures their cholesterol. Which term best describes the 200 adults?

Accepted Answer

Sample

Question 3

Which formula correctly calculates the mean ($$\mu) of a $$population with $$N$$ values $$x_1$$, $$x_2$$, ..., x_N$$?

Accepted Answer

$$\mu = \dfrac{\sum_{i=1}^{N} x_i}{N}$$

Question 4

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

Accepted Answer

Range

Question 5

A pharmaceutical company tests a new drug on two groups: one receives the drug, the other a placebo. What type of study is this?

Accepted Answer

Experimental study

Question 6

Which formula is used to calculate the sample variance $$s^2$$ for a sample of $$n$$ values $$x_1$$, $$x_2$$, ..., x_n$$ with mean $$\bar{x}$$?

Accepted Answer

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

Question 7

A hospital wants to compare the average recovery time for two different treatments. Which statistical test is most appropriate?

Accepted Answer

Two-sample t-test

Question 8

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

Accepted Answer

Type I error is rejecting a true null hypothesis, while Type II error is failing to reject a false null hypothesis.

Question 9

A teacher wants to know if students' test scores are normally distributed. Which graphical method should she use?

Accepted Answer

Histogram

Question 10

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

Accepted Answer

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

Question 11

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.

Question 12

Which of the following is a valid null hypothesis ($$H_0) $$for a test comparing the means of two populations?

Accepted Answer

$$H_0$$: \$$mu_1$$ = \$$mu_2$$

Question 13

A biologist wants to test if the proportion of diseased plants in two fields is the same. Which test should she use?

Accepted Answer

Chi-square test for proportions

Question 14

Which formula is used to calculate the confidence interval for a population mean when the population standard deviation $$\sigma is $$known?

Accepted Answer

$$\bar{x} \pm z^* \dfrac{\sigma}{\sqrt{n}}$$

Question 15

A company wants to know if customer satisfaction differs by region. They collect ratings from four regions. Which statistical method should they use?

Accepted Answer

One-way ANOVA

Question 16

Which of the following best describes the Central Limit Theorem?

Accepted Answer

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

Question 17

A medical researcher wants to test whether a new treatment is more effective than the standard. She sets $$\alpha = 0.05. $$What does $$\alpha$$ represent?

Accepted Answer

The probability of making a Type I error

Question 18

Which formula is used to calculate the sample proportion $$\hat{p}$$ from $$x$$ successes in $$n$$ trials?

Accepted Answer

$$\hat{p} = \dfrac{x}{n}$$

Question 19

A student calculates the mean and median of a dataset and finds they are very different. What does this suggest about the data?

Accepted Answer

The data are likely skewed.

Question 20

Which of the following is the correct formula for the slope ($$b_1) in $$simple linear regression for $$n$$ data points $$(x_i, y_i)$$?

Accepted Answer

$$b_1$$ = \dfrac{\sum_{i=1}^{n} (x_i - \bar{x})(y_i - \bar{y})}{\sum_{i=1}^{n} (x_i - \bar{x}$$)^2$$}$$

Statistics Syllabus and Study Guide: Stat C100 & Math 54C (Santa Monica College)

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