This question is incomplete, the complete question is;
Your friend Mona claims that the average student debt immediately after graduation in the United States is $24,500. You want to see if your university has lower student debt at graduation. To test this, you randomly collect data from 40 students who recently graduated. The average of your sample is $22,413, with an associated standard deviation of $7,312. Using this data to perform the hypothesis test; H₀ : μ = 24,500 vs Hₐ : μ < 24,500.
What is the p-value of this test and conclusion at ∝ = 0.05
Answer:
a) p-value = 0.0394
b) Since p value ( 0.0394 ) is less than ∝ ( 0.05 ), We reject the null hypothesis.
Hence, There is insufficient evidence at ∝ = 0.05 to claim that the average student debt immediately after graduation in the United States is $24,500.
Explanation:
Given the data in the question;
sample size n = 40
sample mean x' = 22413
level of significance ∝ = 0.05
standard deviation s = 7312
Hypothesis;
Null Hypothesis H₀ : μ = 24,500
Alternative Hypothesis Hₐ : μ < 24,500
Test Statistics;
t = (x' - μ) / ( s/√n)
we substitute
t = (22413 - 24500) / ( 7312 / √40)
t = -2087 / 1156.1287
t = -1.805
Degree of Freedom DF = n - 1 = 40 - 1 = 39
With t = -1.8052 and df = 39
p( t < -1.805 ) = 0.0394
p-value = 0.0394
Since p value ( 0.0394 ) is less than ∝ ( 0.05 ), We reject the null hypothesis.
Hence, There is insufficient evidence at ∝ = 0.05 to claim that the average student debt immediately after graduation in the United States is $24,500.