Q: A researcher wants to estimate the proportion of students who prefer online classes. If the sample proportion is $$\hat{p} = 0.6$$ and the sample size is $$n = 100$$, what is the standard error of $$\hat{p}$$?

$$SE(\hat{p}) = \sqrt{\frac{0.6 \times 0.4}{100}}$$

Question 1

Which of the following formulas correctly represents the standard error of the sample mean $$\bar{x}$$ when estimating the population mean $$\mu$$?

Accepted Answer

$$SE(\bar{x}) = \frac{s}{\sqrt{n}}$$

Question 2

A researcher wants to estimate the proportion of students who prefer online classes. If the sample proportion is $$\hat{p} = 0.6$$ and the sample size is $$n = 100$$, what is the standard error of $$\hat{p}$$?

Accepted Answer

$$SE(\hat{p}) = \sqrt{\frac{0.6 	imes 0.4}{100}}$$

Question 3

Which parameter is estimated by the statistic $$b_1 in a $$simple linear regression model?

Accepted Answer

$$\$$beta_1$$

Question 4

If you are comparing the means of two independent samples, which formula should you use for the standard error?

Accepted Answer

$$SE(\bar{x}_1 - \bar{x}_2) = \sqrt{\frac{s_1$^2}{n_1$} + \frac{s_2$^2}{n_2$}}$$

Question 5

A pharmaceutical company tests a new drug on the same group of patients before and after treatment. Which standard error formula is appropriate for the mean difference?

Accepted Answer

$$SE(\bar{x}_d) = \frac{s_d}{\sqrt{n_d}}$$

Question 6

In the context of regression analysis, what does $$SE(b_1$)$$ measure?

Accepted Answer

The standard error of the estimated slope coefficient

Question 7

A sample of 64 patients has a sample mean cholesterol level of 200 mg/dL with a sample standard deviation of 32 mg/dL. What is the standard error of the mean?

Accepted Answer

$$SE(\bar{x}) = \frac{32}{\sqrt{64}} = 4$$

Question 8

Which of the following is NOT a correct pairing of parameter and its sample statistic?

Accepted Answer

Population mean $$\mu$$ and sample proportion $$\hat{p}$$

Question 9

A study compares the average test scores of two independent classes. Class 1 has $$n_1 = 30$, s_1$ = 10$$; Class 2 has $$n_2 = 40$, s_2$ = 12. $$What is the standard error for the difference in means?

Accepted Answer

$$SE(\bar{x}_1 - \bar{x}_2) = \sqrt{\frac{10^2$}{30} + \frac{12^2$}{40}}$$

Question 10

If $$s^2 = 25$ and SS$$_{XX} = 100$$, what is the standard error of the slope estimate b_1$ in a regression analysis?

Accepted Answer

$$SE(b_1$) = \sqrt{\frac{25}{100}} = 0.5$$

Question 11

Which formula would you use to calculate the standard error for the mean difference in a paired sample (e.g., before and after measurements on the same subjects)?

Accepted Answer

$$SE(\bar{x}_d) = \frac{s_d}{\sqrt{n_d}}$$

Question 12

A poll finds that 55% of voters support a candidate, based on a sample of 400 voters. What is the standard error of the sample proportion?

Accepted Answer

$$SE(\hat{p}) = \sqrt{\frac{0.55 	imes 0.45}{400}}$$

Question 13

Which of the following scenarios would require the use of $$SE(\bar{x}_1 - \bar{x}_2)$$?

Accepted Answer

Comparing the average blood pressure between two independent groups

Question 14

If the sample size increases, what happens to the standard error of the mean?

Accepted Answer

It decreases

Question 15

Which formula would you use to estimate the standard error of a sample proportion?

Accepted Answer

$$SE(\hat{p}) = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$

Standard Errors for Common Statistics: Parameters, Estimators, and Formulas

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