Question

Suppose that Crown Bottling Company decides to use a level of significance of α = 0.01, and suppose a random sample of 39 bottle fills is obtained from a test run of the filler. For each of the following four sample means— x ¯ x¯ = 16.05, x ¯ x¯ = 15.95, x ¯ x¯ = 16.03, and x ¯ x¯ = 15.97 — determine whether the filler’s initial setup should be readjusted. In each case, use a critical value, a p-value, and a confidence interval. Assume that σ equals .1. (Round your z to 2 decimal places and p-value to 4 decimal places and CI to 3 decimal places.) , sample mean is 16.05 what is the z and p value? CI? sample mean is 15.95, what is the z value, p value and CI? sample mean is 16.03, what is the z value, p value, and CI? sample mean is 15.97, what is the z value, p value, and CI? population mean is 16

Answer 1

To determine the z-value, p-value, and confidence interval for each sample mean, use the formula z = (x - μ) / (σ / sqrt(n)). Calculate the z-value by plugging in the values for x, μ, σ, and n. Find the p-value using a standard normal distribution table or calculator, and determine the confidence interval using the formula CI = x ± (z * (σ / sqrt(n))).

Step-by-step explanation:

To determine the z-value, p-value, and confidence interval for each of the four sample means, we can use the formula:

z = (x - μ) / (σ / sqrt(n))

where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

For example, for the sample mean of 16.05:

z = (16.05 - 16) / (0.1 / sqrt(39)) = 0.7071

The corresponding p-value can be calculated using a standard normal distribution table or a calculator. The confidence interval can be determined using the formula:

CI = x ± (z * (σ / sqrt(n)))

For example, for the sample mean of 16.05:

CI = 16.05 ± (1.645 * (0.1 / sqrt(39)))