Question

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

Answer 1

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.

Step-by-step 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.