A carpet company advertises that it will deliver your carpet

A carpet company advertises that it will deliver your carpet within 15 days of purchase. A sample of 49 past customers is taken. The average delivery time in the sample was 16.6 days. Assume the population standard deviation is known to be 5.6 days. Answer the following questions:

1. What is the cut-off point at alpha = .05?
2. What is the cut-off point if Type I error is 1%?
3. Would you reject the Null at 5% level of significance?
4. Would you reject the Null at 1% level of significance?
5. If suppose the true delivery time for the population is 17 days. What is the Type II error at Alpha = .01?
6. If suppose the true delivery time for the population is 17 days. What is the Type II error at Alpha = .05?

Answer choices:

a) 19.62%
b) Yes
c) 16.864
d) 43.25%
e) 16.316
f) No

Please show how to solve these.

Solution

Set Up Hypothesis
Null Hypothesis H0: U<=15
Alternate Hypothesis H1: U>15
Test Statistic
Population Mean(U)=15
Given That X(Mean)=16.6
Standard Deviation(S.D)=5.6
Number (n)=49
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=16.6-15/(5.6/Sqrt(49)
Zo =2
| Zo | =2

AT 0.05 LOS
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =2 & | Z | =1.64
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value : Right Tail - Ha : ( P > 2 ) = 0.0228
Hence Value of P0.05 > 0.0228, Here we Reject Ho

company advertises does n\'t deliver your carpet within 15 days of purchase

AT 0.01 LOS
Critical Value
The Value of |Z | at LOS 0.01% is 2.33
We got |Zo| =2 & | Z | =2.33
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value : Right Tail - Ha : ( P > 2 ) = 0.0228
Hence Value of P0.01 < 0.0228, Here We Do not Reject Ho
company advertises will deliver your carpet within 15 days of purchase

ANS:
1. ( P > 2 ) = 0.0228
3. Yes, We Reject at 0.05
4. No, We Accept at 0.01