Q: Which formula is used to calculate the expected frequency in a chi-square test for independence?

$$E = \frac{(\text{row total}) \times (\text{column total})}{\text{grand total}}$$

Question 1

Which of the following best describes the primary purpose of statistics in scientific research?

Accepted Answer

To summarize, analyze, and interpret data to draw meaningful conclusions

Question 2

A medical researcher wants to determine if a new drug lowers blood pressure more effectively than the current standard. Which statistical concept is MOST important for ensuring the results are not due to random chance?

Accepted Answer

Statistical significance

Question 3

Which formula is used to calculate 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 4

A teacher wants to know if students who study with online videos perform better than those who use textbooks. Which statistical test should be used to compare the average scores of the two groups?

Accepted Answer

Independent samples t-test

Question 5

If the standard deviation of a dataset is zero, what does this indicate about the data?

Accepted Answer

All data values are the same

Question 6

Which of the following is the correct formula for the sample variance $$s^2$$?

Accepted Answer

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

Question 7

A hospital administrator wants to know if the average wait time in the emergency room has changed after a new policy was implemented. Which type of hypothesis test should be used?

Accepted Answer

One-sample t-test

Question 8

Which of the following statements about the p-value in hypothesis testing is TRUE?

Accepted Answer

A p-value less than 0.05 suggests evidence against the null hypothesis

Question 9

A researcher collects the following data: 2, 4, 4, 6, 8. What is the median of this dataset?

Accepted Answer

4

Question 10

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

Accepted Answer

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

Question 11

A company wants to estimate the proportion of customers satisfied with their service. Which formula should be used to calculate the confidence interval for a population proportion $$p$$?

Accepted Answer

$$\hat{p} \pm z^* \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$

Question 12

Which of the following is NOT an assumption of the independent samples t-test?

Accepted Answer

The samples are paired

Question 13

A biologist is testing whether a new fertilizer increases plant growth. She measures the height of 30 plants with and without fertilizer. Which statistical test should she use?

Accepted Answer

Paired samples t-test

Question 14

Which formula is used to calculate the correlation coefficient $$r$$ for 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 15

A student scores 1.5 standard deviations above the mean on a standardized test. What is her z-score?

Accepted Answer

1.5

Question 16

Which formula is used to calculate the expected frequency in a chi-square test for independence?

Accepted Answer

$$E = \frac{(	ext{row total}) 	imes (	ext{column total})}{	ext{grand total}}$$

Question 17

A researcher wants to test if the mean cholesterol level in a population is different from 200 mg/dL. She collects a sample and calculates a test statistic. Which formula should she use for the one-sample t-test?

Accepted Answer

$$t = \frac{\bar{x} - \mu_0$}{s / \sqrt{n}}$$

Question 18

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

Question 19

A psychologist wants to compare the average anxiety scores of three different therapy groups. Which statistical test should she use?

Accepted Answer

ANOVA

Question 20

Which formula is used to calculate the margin of error for a confidence interval for the mean when the population standard deviation is known?

Accepted Answer

$$E = z^* \frac{\sigma}{\sqrt{n}}$$

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