Question 1

Which formula is used to calculate the 95% confidence interval estimate for a population proportion $$p$$ when the sample proportion is $$\hat{p}$$ and the sample size is $$n$$?

Accepted Answer

$$\hat{p} \pm 1.96 \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$$

Question 2

A pharmaceutical company wants to estimate the proportion of patients experiencing adverse reactions to a new drug. In a sample of 1500 patients, 24 had adverse reactions. What is the sample proportion $$\hat{p}$$?

Accepted Answer

$$\hat{p} = \dfrac{24}{1500} = 0.016$$

Question 3

Which of the following best describes the margin of error (ME) for a population proportion?

Accepted Answer

It is the maximum likely difference between the observed sample proportion and the true value of the population proportion.

Question 4

If the population proportion $$p is $$unknown, what conservative value is often used for $$p$$ when calculating sample size for a proportion?

Accepted Answer

$$p = 0.50$$

Question 5

A researcher wants to estimate the mean systolic blood pressure of adults in a city. The sample mean is 130 mmHg, the sample standard deviation is 15 mmHg, and the sample size is 36. What is the 95% confidence interval for the population mean?

Accepted Answer

$$130 \pm 1.96 \dfrac{15}{\sqrt{36}}$$

Question 6

Which statement about the sample mean $$\bar{x} is $$correct?

Accepted Answer

The sample mean $$\bar{x} is $$the best point estimate of the population mean $$\mu.$$

Question 7

A 95% confidence interval for a population proportion $$p is $$calculated as (0.381, 0.497). What does this interval mean?

Accepted Answer

We are 95% confident that the true population proportion $$p$$ lies between 0.381 and 0.497.

Question 8

Which formula is used to determine the required sample size $$n$$ for estimating a population proportion with a specified margin of error $$E$$ and confidence level $$z_{\alpha/2}$$?

Accepted Answer

$$n = \dfrac{z_{\alpha/2}^2 p (1-p)}{E^2$}$$

Question 9

When constructing a confidence interval for the population mean and the population variance is unknown, which distribution is used?

Accepted Answer

The $$t-$$distribution

Question 10

A study finds that 122 out of 280 patients were correctly classified. Construct a 95% confidence interval for the proportion of correct classifications. What is the sample proportion $$\hat{p}$$?

Accepted Answer

$$\hat{p} = \dfrac{122}{280} \approx 0.436$$

Question 11

Which of the following is NOT a requirement for using the normal approximation to construct a confidence interval for a population proportion?

Accepted Answer

The sample mean is greater than the sample standard deviation

Question 12

What is the degrees of freedom for a $$t-$$distribution when estimating the mean from a sample of size $$n$$?

Accepted Answer

$$df = n - 1$$

Question 13

A researcher wants to estimate the population variance $$\$$sigma^2$$ using a sample of size n$. Which formula gives the sample variance s^2$?

Accepted Answer

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

Question 14

Which of the following best describes a point estimate?

Accepted Answer

A single value used to estimate a population parameter.

Question 15

In the context of confidence intervals, what does a 99% confidence level mean?

Accepted Answer

If we repeated the sampling process many times, about 99% of the intervals would contain the true population parameter.

Question 16

A sample of 10 measurements of a rare bird's wingspan yields a mean of 14.6 cm and a sample standard deviation of 1.2 cm. What is the 95% confidence interval for the population mean?

Accepted Answer

$$14.6 \pm t_{0.025,9} \dfrac{1.2}{\sqrt{10}}$$

Question 17

Which formula is used to construct a confidence interval for the population variance $$\$$sigma^2$$ using the sample variance s^2$ and the $$\$$chi^2$$ distribution?

Accepted Answer

$$\left( \dfrac{(n-1)s^2$}{\$$chi^2$$_{\alpha/2}}, \dfrac{(n-1)s^2$}{\$$chi^2$$_{1-\alpha/2}} \right)$$

Question 18

Suppose you want to estimate the proportion of voters who support a new policy. You want a margin of error of 0.03 at a 95% confidence level. What sample size should you use, assuming $$p = 0.5$$?

Accepted Answer

$$n = \dfrac{(1.96)^2$ 	imes 0.5 	imes 0.5}{(0.03)^2$}$$

Question 19

Which of the following is true about the interpretation of a confidence interval for a population parameter?

Accepted Answer

The interval provides a range of plausible values for the population parameter, based on the sample data.

Estimating Parameters and Determining Sample Sizes: Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard