Q: A sample of 30 students has a mean test score of 75 and a standard deviation of 10. What is the 95% confidence interval for the mean test score? (Assume normality and use $$ z_{0.025} = 1.96 )$$

$$ 75 \pm 1.96 \times \frac{10}{\sqrt{30}} $$

Question 1

Which of the following best describes the purpose of inferential statistics?

Accepted Answer

To estimate population parameters and make predictions based on sample data.

Question 2

A pharmaceutical company wants to test whether a new drug lowers blood pressure more effectively than the current standard. Which statistical test should they use to compare the mean blood pressure reduction between two independent groups?

Accepted Answer

Student's t-test for independent samples

Question 3

Given a dataset with values: 2, 4, 6, 8, 10, what is the standard deviation?

Accepted Answer

$$ \sqrt{8} \approx 2.83 $$

Question 4

Which formula represents the sample mean $$ \bar{x} $$ for a dataset with $$ n $$ values $$ x_1$, x_2$, ..., x_n $$?

Accepted Answer

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

Question 5

A researcher wants to estimate the proportion of students who prefer online classes. Which formula should be used to construct a 95% confidence interval for the population proportion $$ p $$?

Accepted Answer

$$ \hat{p} \pm z_{\alpha/2} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} $$

Question 6

Which of the following is NOT an assumption for performing a linear regression analysis?

Accepted Answer

The independent variable is categorical.

Question 7

A hospital administrator wants to determine if there is a significant association between patient gender (male/female) and recovery outcome (recovered/not recovered). Which statistical test is most appropriate?

Accepted Answer

Chi-square test of independence

Question 8

If the probability of a patient having a certain disease is 0.2, what is the probability that, in a random sample of 5 patients, exactly 2 have the disease? (Assume independence.)

Accepted Answer

$$ \binom{5}{2} (0.2)^2$ (0.8)^3$ $$

Question 9

Which measure of central tendency is most appropriate for summarizing the salaries of employees in a company where a few executives earn much higher salaries than the rest?

Accepted Answer

Median

Question 10

A sample of 30 students has a mean test score of 75 and a standard deviation of 10. What is the 95% confidence interval for the mean test score? (Assume normality and use $$ z_{0.025} = 1.96 )$$

Accepted Answer

$$ 75 \pm 1.96 	imes \frac{10}{\sqrt{30}} $$

Question 11

Which formula is used to calculate the Pearson correlation coefficient $$ r $$ between two variables $$ x $$ and $$ y $$?

Accepted Answer

$$ r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2$ \sum (y_i - \bar{y})^2$}} $$

Question 12

A scientist wants to test the hypothesis that the mean weight of a species of fish in a lake is 5 kg. Which is the correct null hypothesis ($$ H_0$ $$)?

Accepted Answer

$$ H_0$: \mu = 5 $$

Question 13

Which formula is used to calculate the variance $$ s^2$  of a $$sample?

Accepted Answer

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

Question 14

In a clinical trial, the p-value for a hypothesis test is 0.03. If the significance level $$ \alpha  is 0.05$$, what should the researcher conclude?

Accepted Answer

Reject the null hypothesis.

Question 15

Which formula is used to calculate the test statistic for a sample mean when the population standard deviation is unknown?

Accepted Answer

$$ t = \frac{\bar{x} - \mu}{s / \sqrt{n}} $$

Question 16

A company wants to compare the average productivity of three departments. Which statistical test should they use?

Accepted Answer

Analysis of variance (ANOVA)

Question 17

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

Accepted Answer

$$ y = a + bx $$

Question 18

A random sample of 100 people is surveyed about their favorite ice cream flavor. Which type of sampling is this?

Accepted Answer

Random sampling

Question 19

Which of the following best describes the concept of dispersion in statistics?

Accepted Answer

The spread or variability of data values.

STAT C1000E: Course Overview and Key Concepts in Statistics

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