On December 1, 2013, Jeff Bezos (Founder and CEO of Amazon.com) announced on CBS's "60 minutes" that his company plans to develop a "delivery drone" that would cut delivery time for products purchased on Amazon.com to an average of 30 minutes or less. Assume that a random sample of 50 deliveries made by a prototype of the drone had an average delivery time of 32.1 minutes with a standard deviation of 5.4 minutes.

a)Test whether this sample provides sufficient evidence against Bezos' claim at the 5% level of significance. What is the p-value of this test and how does it relate to your conclusion?

b)Now use the same data to perform the same test at the 1% level of significance. Did your conclusion change? Did the p-value change? Why, why not?

the solution the website show :

Explanation:

Standard delivery time = 60 minutes

Claim : cut 30 minutes or less

New delivery time = 60 - 30 or less = 30 or greater

n = 50

x = 32.1

s = 5.4

= 30

(a) Hypothesis :

Ho : = 30

H1 : > 30

Test statistics :

t = (x - )/(s/n)

t = (32.1 - 30)/(5.4/50)

t = 2.75

P - value :

We can't find p - value using R

df = n - 1 = 50 - 1 = 49

t = 2.75

P value = 0.004162 = 0.0042

Decision :

Since, P value = 0.0042 < = 0.05

Hence, we reject Ho at = 0.05

Conclusion :

There is sufficient evidence to support the claim that drone delivery cut delivery time on average 30 minutes or less.

(b) Since, P value = 0.0042 > = 0.01

Hence, we tail to reject Ho at = 0.01

And yes, at 1% significance level, conclusion will change.

P value will not be change because P value is independent of significance level.

But in answer (b) p value 0.0042 is actually lower than 0.01, I think this answer is wrong.