Q: A sample of 100 students has a mean score of 75 and a standard deviation of 10. What is the 95% confidence interval for the mean? (Use $$z = 1.96)$$

$$75 \pm 1.96 \times \frac{10}{\sqrt{100}}$$

Question 1

Which of the following best describes the purpose of organizing and graphing data in statistics?

Accepted Answer

To visually summarize and reveal patterns or trends in the data.

Question 2

A researcher wants to compare the average test scores of two different classes. Which statistical method is most appropriate for this scenario?

Accepted Answer

Hypothesis testing

Question 3

Which formula is used to calculate the sample mean $$\bar{x}$$ for a dataset with $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

$$\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$$

Question 4

Which of the following is NOT a property of the normal distribution?

Accepted Answer

It has a skewness greater than zero.

Question 5

A hospital administrator wants to estimate the average length of stay for patients. Which concept allows her to use a sample to make inferences about the population mean?

Accepted Answer

Sampling distribution of the sample mean

Question 6

Given a dataset: 2, 4, 4, 6, 8. What is the variance $$s^2 of $$the sample?

Accepted Answer

$$s^2 = 5.5$

Question 7

Which equation represents the linear regression line for predicting $$y$$ from $$x$$?

Accepted Answer

$$y = a + bx$$

Question 8

A pharmaceutical company tests a new drug and finds a $$p-$$value of 0.03 when comparing it to a placebo. If the significance level is $$\alpha = 0.05$$, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis; there is evidence the drug is effective.

Question 9

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 10

Which of the following best describes the difference between descriptive and inferential statistics?

Accepted Answer

Descriptive statistics summarize data; inferential statistics make predictions or generalizations about a population.

Question 11

A sample of 100 students has a mean score of 75 and a standard deviation of 10. What is the 95% confidence interval for the mean? (Use $$z = 1.96)$$

Accepted Answer

$$75 \pm 1.96 	imes \frac{10}{\sqrt{100}}$$

Question 12

Which of the following is a correct interpretation of a correlation coefficient $$r = -0.85$$ between hours studied and number of errors on an exam?

Accepted Answer

There is a strong negative linear relationship; as hours studied increase, errors decrease.

Question 13

Which formula is used to calculate the probability of event $$A or $$event $$B$$ occurring, if $$A$$ and $$B$$ are mutually exclusive?

Accepted Answer

$$P(A \cup B) = P(A) + P(B)$$

Question 14

A factory produces light bulbs, and 2% are defective. If you randomly select 50 bulbs, which distribution best models the number of defective bulbs?

Accepted Answer

Binomial distribution

Question 15

Which formula is used to calculate the sum of squares $$SS$$ for a sample with $$n$$ observations and mean $$\bar{x}$$?

Accepted Answer

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

Question 16

A clinical trial compares two treatments using ANOVA. What is the primary purpose of using ANOVA in this context?

Accepted Answer

To determine if there are statistically significant differences among group means.

Question 17

Which symbolic notation is commonly used to represent the population mean?

Accepted Answer

$$\mu$$

Question 18

A researcher constructs a 99% confidence interval for a population proportion. Compared to a 95% confidence interval, the 99% interval will be:

Accepted Answer

Wider, because higher confidence requires more margin for error.

Question 19

Which of the following is a real-world example of using probability to make decisions?

Accepted Answer

A doctor estimating the likelihood of a patient responding to a treatment.

Elementary Statistics – Course Syllabus and Study Guide

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