At Western University the historical mean of scholarship examination scores for freshman applications is 900. A historical population standard deviation = 180 is assumed known. Each year, the assistant dean uses a sample of applications to determine whether the mean examination score for the new freshman applications has changed.

What is the p-value (to 3 decimals)?

0.006

To calculate the p-value, we need the sample mean and sample size, as well as the population mean and population standard deviation.

Given:
Population mean (μ) = 900
Population standard deviation (σ) = 180

Since the sample size (n) is not provided in the question, we cannot calculate the p-value without this information. Please provide the sample size in order to proceed with the calculation.

To calculate the p-value, we need to conduct a hypothesis test. In this case, we want to determine whether the mean examination score for new freshman applications has changed from the historical mean of 900.

Let's assume that the null hypothesis (H0) is that the mean examination score for new freshman applications is still 900. The alternative hypothesis (Ha) would be that the mean examination score for new freshman applications is different from 900.

Now, we can use the information provided to calculate the test statistic, which is the z-score. The formula for the z-score is:

z = (x - μ) / (σ / √n)

where:
x = sample mean
μ = population mean
σ = population standard deviation
n = sample size

In this case, the population mean (μ) is 900, the population standard deviation (σ) is 180, and the sample size (n) is not given. Since the sample size is not provided, we cannot calculate the z-score directly.

However, we can calculate the z-score using the t-distribution if we know the sample mean and sample size. It seems that the sample mean and sample size are missing from the question, which makes it impossible to calculate the p-value accurately.

Therefore, without the sample mean and sample size, we cannot calculate the p-value needed to answer the question.