Construct a 99% confidence interval about if the sample size n is 34 lower bound upper bound
Lower bound: 0.945
Upper bound: 0.977
To construct a confidence interval with a known sample size, you need to know the sample mean and the standard deviation. However, since you haven't provided those values, I'm unable to give you the exact confidence interval.
Nevertheless, I can explain the general process of constructing a confidence interval. Follow these steps:
1. Determine the significance level: In this case, you need a 99% confidence interval, so the significance level (α) is 1 - 0.99 = 0.01.
2. Find the critical value: The critical value corresponds to the significance level and the distribution of your data. If the sample size is large (>30) and the population follows a normal distribution, you can use the Z-distribution. For a 99% confidence interval, the critical value (Z) is approximately 2.576.
3. Calculate the standard deviation: As you haven't provided the standard deviation (σ), you can either estimate it based on previous data or use the sample standard deviation (s) if you have it. If you have neither, you won't be able to construct a confidence interval without more information.
4. Calculate the standard error: The standard error (SE) represents the variability of the sample mean, and it can be calculated by dividing the standard deviation (σ or s) by the square root of the sample size (n).
SE = σ / √n or SE = s / √n
5. Calculate the margin of error: The margin of error represents the maximum expected difference between the sample mean and the population mean. Multiply the standard error by the critical value to find the margin of error (ME).
ME = Z * SE
6. Calculate the confidence interval: Finally, calculate the confidence interval by subtracting the margin of error from the sample mean to find the lower bound, and adding it to the sample mean to find the upper bound.
Lower Bound = Sample Mean - ME
Upper Bound = Sample Mean + ME
Remember, without the sample mean and standard deviation, I'm unable to provide you with specific values for the confidence interval.