You chose a simple random sample of 300 guests you develop a 95 percent confidence interval estimate you found the following 325 and 32 determine the standard error of the sampling distribution determine the critical value z from the standard normal table compute the confidence interval estimate
To determine the standard error of the sampling distribution, you need to use the formula:
Standard Error = (Standard Deviation) / √(Sample Size)
In this case, the standard deviation is not given. Instead, you are provided with two data points, 325 and 32. It is important to note that the two data points given are not sufficient for calculating the standard error. The standard deviation is a measure of the spread of the data, and without knowing the full dataset, it cannot be determined accurately.
Moving on to the next step, determining the critical value (z) from the standard normal table:
1. The confidence level is given as 95 percent, which means the alpha level (α) is 1 - 0.95 = 0.05.
2. Since the confidence interval is two-tailed, we need to divide the alpha level by 2: α/2 = 0.05/2 = 0.025.
3. Look up the z-score that corresponds to a cumulative probability of 0.975 (1 - 0.025) in the standard normal distribution table.
The z-score for a cumulative probability of 0.975 is approximately 1.96.
Now, we can compute the confidence interval estimate:
1. The formula for a confidence interval estimate is:
Confidence Interval = (Sample Mean) ± (Critical Value * Standard Error)
2. Since the sample mean is not given, it cannot be calculated using the data points provided.
To summarize, without knowing the standard deviation and the sample mean, it is not possible to determine the standard error of the sampling distribution or compute the confidence interval estimate.