A statistics practitioner formulated the following hypothesis:

Ho: population mean=200
H1: population mean<200

sample mean=190
n=9
population standard deviation=50

Calculate the p-value of the test

Use the z-test formula to find the test statistic since you know the population standard deviation:

z = (sample mean - population mean)/(standard deviation divided by the square root of the sample size)

With the data given in the problem:
z = (190 - 200)/(50/√9)

Finish the calculation and determine the p-value using a z-table. The p-value is the actual level of the test statistic.

I hope this will help get you started.

To calculate the p-value for this hypothesis test, you need to perform a t-test. The t-test compares the sample mean to the hypothesized population mean and measures the likelihood of obtaining a sample mean as extreme as the observed one, assuming the null hypothesis is true.

Here are the steps to calculate the p-value:

1. Compute the t-value:
The t-value measures the difference between the sample mean and the hypothesized population mean in terms of standard errors. It is given by the formula:

t = (sample mean - hypothesized mean) / (sample standard deviation / √n)

In this case, the sample mean is 190, the hypothesized mean is 200, the sample standard deviation is 50, and n is 9.

Plugging in these values, we get:
t = (190 - 200) / (50 / √9)
t = -10 / (50 / 3)
t = -10 / 16.67
t ≈ -0.6

2. Determine the degrees of freedom:
The degrees of freedom for this test is given by n - 1, where n is the size of the sample. In this case, n = 9, so the degrees of freedom is 9 - 1 = 8.

3. Find the p-value:
The p-value represents the probability of obtaining a t-value as extreme as the observed one, assuming the null hypothesis is true. We need to consult a t-distribution table or use a statistical software to find the p-value associated with the calculated t-value and degrees of freedom.

Assuming a one-sided alternative hypothesis (H1: population mean < 200), we are looking for the area under the t-distribution curve to the left of the calculated t-value (-0.6).

Using a t-distribution table or software, you can find that the p-value is approximately 0.282.

Therefore, the p-value of the test is approximately 0.282.