Hypothesis Testing

Question

You wish to test the following claim (Ha) at a significance level of α=0.001

Ho:μ=51.9      

Ha:μ>51.9

You believe the population is normally distributed and you know the standard deviation is σ=9.5. You obtain a sample mean of M=54 for a sample of size n=36

What is the test statistic for this sample? (Report answer accurate to three decimal places.)

What is the p-value for this sample? (Report answer accurate to four decimal places.)

Answer 1

The test statistic (z-score) can be calculated using the formula:

z = (M - μ) / (σ/√n)

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

Given M = 54, μ = 51.9, σ = 9.5, and n = 36, we get:

z = (54 - 51.9) / (9.5/√36) = 0.2211

To find the p-value, we look at the z-table or use statistical software to find the probability that a z-score is greater than or equal to 0.221 under the standard normal distribution.

Remember that for a right-tailed test (as indicated by Ha: μ > 51.9), the p-value is the area to the right of the calculated z-score.

Using a standard normal distribution table or statistical software, we find that the area to the left of z = 0.221 is approximately 0.5871.

Since we are interested in the area to the right (for a right-tailed test), we subtract this from 1:

p-value = 1 - 0.5871 = 0.4129

So, the test statistic is 0.221 (rounded to three decimal places) and the p-value is 0.4129 (rounded to four decimal places).