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)?
To determine the p-value, you need to conduct a hypothesis test. The hypothesis test compares the sample mean to the population mean and determines the likelihood of obtaining a sample mean as extreme as the observed value if the null hypothesis is true.
In this case, the null hypothesis (H0) is that there is no change in the mean examination score for the new freshman applications. The alternative hypothesis (Ha) is that there is a change in the mean examination score.
Given that the population standard deviation is assumed known as 180, and assuming the data is normally distributed, you can use the z-test to perform the hypothesis test.
The formula for the z-test is:
z = (x̄ - μ) / (σ / sqrt(n))
Where:
z is the test statistic
x̄ is the sample mean
μ is the population mean
σ is the population standard deviation
n is the sample size
In this case, you haven't provided the sample mean and sample size. Without that information, it is not possible to calculate the p-value.
However, once you have the calculated z-value, you can use a standard normal distribution table (or a statistical software) to find the p-value corresponding to that z-value. The p-value represents the probability of obtaining a test statistic as extreme as the observed result, assuming the null hypothesis is true.