Question

**3) According to the institute for Students in Shackles,
67% of all college students in a recent year graduated with student
loan debt. The University of Central Florida reports that only 52%
of its graduates from a random sample of 500 students have student
loan debt. Use a hypothesis test to determine if there is enough
evidence to support UCF''s claim that their student loan debt is
less. Assume all conditions have been met and proceed with the
hypothesis test.**

**a) State your null and alternative
hypothesis.**

**b) Find the indicated values. Remember to show all work
and report 5 decimal places. Alpha to two decimal
places.**

**p hat:**

**SD:**

**Z:**

**Z*:**

**P-VALUE:**

**c) State your conclusion based on your hypothesis test
in the context of the problem.**

Answer #1

a)

H0: p = 0.67

Ha: p < 0.67

b)

= **0.52**

SD = sqrt [ p( 1 - p) / n ]

= sqrt [ 0.67 ( 1 - 0.67) / 500 ]

= **0.02103**

Z = ( - p) / SD

= ( 0.52 - 0.67) / 0.02103

= **-7.13267**

Z* = from Z table, at
= 0.05 , critical value = **-1.645**

p-value = P(Z < z)

= P(Z < -7.13267)

= **0** (From Z table)

c)

Since p-value < 0.05 , Reject the null hypothesis.

We conclude at 0.05 level that we have sufficient evidence to support the claim that

their student loan debt is less

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