At a certain university, the average cost of books was $370 per student last semester and the population standard deviation was $80. This semester a sample of 45 students revealed an average cost of books of $390 per student. The Dean of Students believes that the costs are greater this semester. What is the test value for this hypothesis?
To determine the test value for this hypothesis, we can use the formula for calculating the standard error (SE) of the sample mean:
SE = Population Standard Deviation / Square Root of Sample Size
In this case, the population standard deviation (σ) is $80, and the sample size (n) is 45.
Let's substitute these values into the formula to calculate the standard error:
SE = 80 / √45
SE ≈ 11.97
The test value, also known as the z-score, can be calculated using the formula:
z = (sample mean - population mean) / SE
The population mean (μ) is given as $370, and the sample mean (x̄) is $390. Substituting these values, along with the standard error, into the formula:
z = ($390 - $370) / 11.97
z ≈ 1.67
Therefore, the test value for this hypothesis is approximately 1.67.
To find the test value for this hypothesis, we can use the formula for calculating the test statistic. The test statistic is a standardized value that helps us determine the likelihood of observing the given sample mean, assuming that the null hypothesis is true.
The formula for the test statistic, also known as the z-score, is given by:
z = (sample mean - population mean) / (population standard deviation / √sample size)
In this case, the population mean is $370, the population standard deviation is $80, and the sample size is 45. The sample mean is $390.
Plugging these values into the formula, we get:
z = ($390 - $370) / ($80 / √45)
Simplifying further:
z = $20 / ($80 / √45)
To calculate this, we first need to find the value of √45. Taking the square root of 45, we get approximately 6.7082.
Now, we can substitute this value into the formula:
z = $20 / ($80 / 6.7082)
z = $20 * (6.7082 / $80)
Simplifying further:
z ≈ $20 * 0.08385125
z ≈ 1.677025
Therefore, the test value for this hypothesis is approximately 1.677025.
Ho: mean = 370
Ha: mean > 370
Z = (score-mean)/SEm = ?
SEm = SD/√n