Question

we know that the sample standard deviation is 6 and the sample size is 20. for what sample mean would the p-value be equal to 0.05? assume that all conditions necessary for inference are satisfied. round your answer to 3 decimal places.

Answer 1

To find the sample mean for which the p-value is equal to 0.05, calculate the z-score corresponding to the desired p-value and solve for the sample mean using the formula for the z-score.

In this case, the sample mean is approximately 1.921.

Step-by-step explanation:

To determine the sample mean, we assume the data is normally distributed, we can use the z-distribution.

The formula for the z-score is: z = (x - μ) / (σ / √n)

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

In this case, the population mean is not given, so we'll assume it to be 0.

th a sample size of 20 and a sample standard deviation of 6, the z-score corresponding to a p-value of 0.05 is approximately 1.645.

Using the formula for the z-score, we can solve for the sample mean:

1.645 = (x - 0) / (6 / √20)

Simplifying the equation:

x = 1.645 * (6 / √20)

Rounding to 3 decimal places, the sample mean for which the p-value is equal to 0.05 is approximately 1.921.