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 calculate the p-value, we need more information, specifically the sample size and the sample mean. The p-value is a measure of the evidence against the null hypothesis, which in this case is that the mean examination score for the new freshman applications has not changed.
Once we have the sample size (n) and the sample mean (x̄), we can use the known population standard deviation (σ = 180) to calculate the test statistic, which is a t-statistic in this case.
The formula to calculate the t-statistic for a one-sample t-test is:
t = (x̄ - μ) / (σ / √n)
Where:
x̄ is the sample mean
μ is the population mean (historical mean of 900)
σ is the population standard deviation (assumed known as 180)
n is the sample size
Using the given historical mean (μ = 900), we can calculate the t-statistic once we have the sample mean (x̄) and the sample size (n).
Please provide the sample mean and the sample size to proceed with the calculation of the p-value.