The National Association of Landscape Professionals has dete

The National Association of Landscape Professionals has determined that on average mulch lasts 87 days befor fading or degrading. Due to an improved production process that extends the life of mulch, the Association believes that there has been an increase in the useful life of standard pine bark mulch. A sample of 36 yards of mulch showed an average life of 88.5 days before it began to fade. Assume from past information that it is known that the standard deviation of the population is 9 days.

A) Give the Null and Alternative Hypotheses

B) Compute the test statistic

C) At 99% confidence using the critical value approach, test the management\'s belief

D) What is the p-value associated with the sample results? What is the conclusion based on the p-value ?

Solution

Set Up Hypothesis
Null, H0: U=87
Alternate, increase in the useful life of standard pine bark mulch H1: U>87
Test Statistic
Population Mean(U)=87
Given That X(Mean)=88.5
Standard Deviation(S.D)=9
Number (n)=36
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=88.5-87/(9/Sqrt(36)
Zo =1
| Zo | =1
Critical Value
The Value of |Z | at LOS 0.01% is 2.33
We got |Zo| =1 & | Z | =2.33
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho

[ANSWERS]
1. H0: U=87 , H1: U>87
2. Zo =1
3. Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho

4.P-Value : Right Tail - Ha : ( P > 1 ) = 0.1587
Hence Value of P0.01 < 0.1587, Here We Do not Reject Ho