Question 9 Practice similar questions
Score: 0 of 5 points
Suppose a population parameter is known to have a standard deviation of 1 .
If the researchers want to be confident that the sample mean is within 0.3 of the true population mean, what sample size should be used?
Enter your answer

Question

Question 9 Practice similar questions
Score: 0 of 5 points
Suppose a population parameter is known to have a standard deviation of 1 .
If the researchers want to be

confident that the sample mean is within 0.3 of the true population mean, what sample size should be used?

Enter your answer

UpStudy AI · Accepted Answer

Determine the sample size using the formula

$$
n = \left(\frac{z \sigma}{E}\right)^2,
$$

where:
- $$ z $$ is the critical value for a $$ 95\% $$ confidence level,
- $$ \sigma $$ is the population standard deviation,
- $$ E $$ is the margin of error.

Given:
- $$ z = 1.96 $$,
- $$ \sigma = 1 $$,
- $$ E = 0.3 $$.

Substitute into the formula:

$$
n = \left(\frac{1.96 \times 1}{0.3}\right)^2 = \left(\frac{1.96}{0.3}\right)^2.
$$

Calculate the quotient:

$$
\frac{1.96}{0.3} \approx 6.5333.
$$

Square the result:

$$
n \approx (6.5333)^2 \approx 42.6844.
$$

Since the sample size must be a whole number and to ensure the margin of error does not exceed $$ 0.3 $$, round up to the next integer:

$$
n = 43.
$$
The required sample size is 43.

Question 9 Practice similar questions
Score: 0 of 5 points
Suppose a population parameter is known to have a standard deviation of 1 .
If the researchers want to be confident that the sample mean is within 0.3 of the true population mean, what sample size should be used?
Enter your answer

Upstudy AI Solution

Answer

Solution

Mind Expander

Related Questions

Latest Statistics Questions

Question 9 Practice similar questions Score: 0 of 5 points Suppose a population parameter is known to have a standard deviation of 1 . If the researchers want to be confident that the sample mean is within 0.3 of the true population mean, what sample size should be used? Enter your answer

Upstudy AI Solution

Answer

Solution

Mind Expander

Related Questions

Latest Statistics Questions

Question 9 Practice similar questions
Score: 0 of 5 points
Suppose a population parameter is known to have a standard deviation of 1 .
If the researchers want to be confident that the sample mean is within 0.3 of the true population mean, what sample size should be used?
Enter your answer