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

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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

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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