Question

In a random sample of 100 LMC students, 32 report reading the LMC Experience regularly. Use a 95%

confidence interval to estimate the percentage of all LMC students who read the LMC Experience
regularly.
Round the standard error to 2 decimal places.
O We should not calculate the 95% confidence interval because normality conditions are not met.
O We are 95% confident that between 27% to 37% of LMC students read the Experience.
O We are 95% confident that between 22% and 42% of all LMC students read the LMC Experience regularly.

Answer 1

We are 95% confident that between 22% and 42% of all LMC students read the LMC Experience regularly. Option 3

How to estimate the percentage of all LMC students

To estimate the percentage of all LMC students who read the LMC Experience regularly, use a 95% confidence interval based on the given random sample of 100 LMC students, where 32 report reading the LMC Experience regularly.

To calculate the confidence interval, calculate the standard error. The formula for the standard error of a proportion is:

Standard Error =
`\sqrt((\hat{p} * (1 - (\hat{p})) / n)`

Where
`\hat{p}` is the sample proportion (32/100) and n is the sample size (100).

`\hat{p}` = 32/100 = 0.32

n = 100

Standard Error =
`\sqrt`((0.32 * (1 - 0.32)) / 100) ≈ 0.048

Rounding the standard error to 2 decimal places, we get 0.05.

Now, calculate the 95% confidence interval using the formula:

Confidence Interval =
`\hat{p}` ± (Z * SE)

Where
`\hat{p}` is the sample proportion, Z is the Z-score corresponding to the desired confidence level (95% in this case), and SE is the standard error.

For a 95% confidence level, the Z-score is approximately 1.96.

Confidence Interval = 0.32 ± (1.96 * 0.05)

Calculating the confidence interval:

Lower bound = 0.32 - (1.96 * 0.05) ≈ 0.22

Upper bound = 0.32 + (1.96 * 0.05) ≈ 0.42

Therefore, we can say with 95% confidence that the percentage of all LMC students who read the LMC Experience regularly is estimated to be between 22% and 42%. Hence, the correct statement is:

We are 95% confident that between 22% and 42% of all LMC students read the LMC Experience regularly.