1 A carpet company advertises that it will deliver your carp

1. 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 16.2 days. The standard deviation of the population (a) is known to be 5.6 days. a. State the null and alternative hypotheses. b. Using the critical value approach, test to determine if their advertisement is legitimate. Let a=0.05 c. Using the p-value approach, test the hypotheses at the 5% level of significance.

Solution

Set Up Hypothesis
Null Hypothesis H0: U=15
Alternate Hypothesis H1: U!=15
Test Statistic
Population Mean(U)=15
Given That X(Mean)=16.2
Standard Deviation(S.D)=5.6
Number (n)=49
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=16.2-15/(5.6/Sqrt(49)
Zo =1.5
| Zo | =1.5
Critical Value
The Value of |Z | at LOS 0.05% is 1.96
We got |Zo| =1.5 & | Z | =1.96
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value : Two Tailed ( double the one tail ) - Ha : ( P != 1.5 ) = 0.1336
Hence Value of P0.05 < 0.1336, Here We Do not Reject Ho

yes, the advertisement is legtimate