Question

The average student loan debt is reported to be $25,235. A student belives that the student loan debt is higher in her area. She takes a random sample of 100 college students in her area and determines the mean to be $27,524 and the standard devition to be $6000. Is there sufficient evidence to support the student' claim at a 5% significance level?

a) Determine the null and alternative hypotheses.

H0H0: μ=μ=

HaHa: μμSelect an answer < not = >   (Put in the correct symbol and value)

b) Determine the test statistic. Round to two decimals.

t=t=

c) Find the p-value. Round to 4 decimals.

P-value =

d) Make a decision.

• Reject the null hypothesis
• Fail to reject the null hypothesis

e) Write the conclusion.

• There is not sufficient evidence to support the claim that student loan debt is higher than $25,235.
• There is sufficient evidence to support the claim that student loan debt is higher than $25,235.

Answer 1

using excel >addin>phstat>two sample t

we have

t Test for Hypothesis of the Mean
Data
Null Hypothesis                m=	25235
Level of Significance	0.05
Sample Size	100
Sample Mean	27524
Sample Standard Deviation	6000
Intermediate Calculations
Standard Error of the Mean	600
Degrees of Freedom	99
t Test Statistic	3.815
Upper-Tail Test
Upper Critical Value	1.660391156
p-Value	0.000118567
Reject the null hypothesis

a) Determine the null and alternative hypotheses.

H0: μ=25235
Ha: μ >25235
b) the test statistic

t=3.82

c) the p-value

P-value =0.0001

d) Make a decision.

• Reject the null hypothesis

e) Write the conclusion.

• There is sufficient evidence to support the claim that student loan debt is higher than $25,235.