Question

A researcher is funded to obtain an estimate for the population proportion of smokers who have tried using e-cigarettes. She plans to interview 100 smokers. Previous studies have estimated that 20% of smokers have tried e-cigarettes. She finds that 23% of smokers have tried e-cigarettes. Which of the following is correct? 0.23 is the population proportion The margin of error for a 95% confidence interval is 8% The standard error of the sample proportion is 0.177 This is a biased estimate because it is based on smokers none of the above

Answer 1

The correct statement is that 0.23 is the sample proportion, the margin of error for a 95% confidence interval is 8%, the standard error of the sample proportion is 0.035, and this is a biased estimate because it is based on a sample of smokers.

Step-by-step explanation:

The correct statement is that 0.23 is the sample proportion, not the population proportion. The margin of error for a 95% confidence interval can be calculated using the formula:

Margin of Error = Critical Value * Standard Error

In this case, the margin of error is 8%, not 8.3%. The correct statement is that the margin of error for a 95% confidence interval is 8%.

The standard error of the sample proportion can be calculated using the formula:

Standard Error = sqrt((Sample Proportion * (1 - Sample Proportion)) / Sample Size)

In this case, the standard error is 0.035, not 0.177. The correct statement is that the standard error of the sample proportion is 0.035.

This is a biased estimate because it is based on a sample of smokers, not the entire population of smokers. Therefore, the correct statement is none of the above.

Answer 2

Complete Question

A researcher is funded to obtain an estimate for the population proportion of smokers who have tried using e-cigarettes. She plans to interview 100 smokers. Previous studies have estimated that 20% of smokers have tried e-cigarettes. She finds that 23% of smokers have tried e-cigarettes.

Which of the following is correct?

A

0.23 is the population proportion

B

The margin of error for a 95% confidence interval is 8%

C

The standard error of the sample proportion is 0.177

D

This is a biased estimate because it is based on smokers none of the above

Answer:

The correct option is B

Step-by-step explanation:

From the question we are told that

The sample size is n = 100

The population proportion is p = 0.20

The sample proportion is
`\r p = 0.23`

Generally the standard error is mathematically represented as

`SEp = \sqrt{(\r p(1 - \r p))/(n) }`

=>
`SEp = \sqrt{(0.23 (1 - 0.23))/(100) }`

=>
`SEp = 0.04208`

Generally for a 95% confidence level is level of significance is

`\alpha = (100 - 95)\%`

`\alpha = 5\%`

`\alpha = 0.05`

Now the critical value of
`(\alpha )/(2)` obtained from the normal distribution table is

`Z_{(\alpha )/(2) } = 1.96`

Generally the percentage margin of error is mathematically represented as

`E = Z_{(\alpha )/(2) } * SE_p * 100`

`E = 1.96* 0.04208 * 100`

`E = 8\%`