Question

We are interested in how long on average it takes Deadpool to grow back a leg. A simple random sample of 25 occasions results in an average of 63 minutes before Deadpool's leg grows back. Assume that the standard deviation of all grow-back-times is 10 minutes.

A. The 80% confidence interval for Deadpool's average time to grow back a leg is ( ,  ). (Answers to two places after the decimal.)

B. Unless our sample is among the most unusual 5% of samples, Deadpool's average time to grow back a leg is between ( ) and ( ) . (Answers to two places after the decimal.)

C. Vanessa claims that average, it takes Deadpool 65 minutes to grow back a leg. Do we have evidence that she's exaggerating the truth at each of the following levels?
The associated p-value for this hypothesis test is ( ) (Answers to four places after the decimal.)

At the 15% level:

At the 13% level:

At the 10% level:

At the 7% level:

At the 5% level:

At the 3% level:

At the 2% level:

At the 1% level:

At the 0.2% level:

At the 0.1% level:

D. Colossus claims that average, it takes Deadpool 65 minutes to grow back a leg. Do we have evidence that he's mistaken at each of the following levels?
The associated p-value for this hypothesis test is ( ) (Answers to four places after the decimal.)
- At the 20% level:

- At the 15% level:

- At the 13% level:

- At the 10% level:

- At the 7% level:

- At the 5% level:

- At the 3% level:

- At the 2% level:

- At the 1% level:

- At the 0.2% level:

- At the 0.1% level:

Answer 1

a)
(Xbar +- z* sigma/sqrt(n))

z= 1.282 for 80% CI

xbar   63.0000
sd   10.000
n   25
alpha   0.2
  
z   1.282
  
SE   2.0000
ME   2.5631
  
lower   60.44
upper   65.56

80% CI is
(60.44 ,65.56 )

B)
z = 1.96 for 0.05 level
95% CI is (59.08,66.92)

c)
Ho : mu = 65
Ha: mu < 65

TS = (Xbar - mu)/(sigma/sqrt(n))
= -1

p-value= P(Z < TS)
= 0.159

if p-value < alpha ,we reject the null hypothesis

hence all level less than 0.159

D) this is 2-tailed
p-value = 0.317

hence all level less than 0.317

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