Question

The Japanese harvester beetle has infected several forests in the Northwest. Official estimates are that 17% of trees are infected. You are a park ranger who has been seeing a lot of these beetles lately, and you think the rate is higher in your area. You check 400 trees around your cabin and find that 79 of them are infected.

• Go through the steps on the Hypothesis Test Guide (D2L). List each step like Step 1, Step 2, etc.
• Please check the conditions using complete sentences.
• Please do the calculations out the long way, but definitely use GeoGebra or a calculator stats package to check.
• Even if the conditions aren’t met, do the rest anyway.
• Use α = 0.03

Answer 1

step 1)

Ho :   p =    0.17                  
H1 :   p ╪   0.17       (Two tail test)          
                          
step 2) Level of Significance,   α =    0.03                 

step 3)

np=0.17*400=68>5

n(1-p) = 332>5

At least 5 expected successes and 5 expected failures in sample. Normality assumption okay.              

Number of Items of Interest,   x =   79                  
Sample Size,   n =    400                  
                          
Sample Proportion ,    p̂ = x/n =    0.1975                  
                          
Standard Error ,    SE = √( p(1-p)/n ) =    0.0188                  
Z Test Statistic = ( p̂-p)/SE = (   0.1975   -   0.17   ) /   0.0188   =   1.4642
                          

step 4)   
p-Value   =   0.1431   [excel formula =2*NORMSDIST(z)]              

step 5)

Decision:   p value>α ,do not reject null hypothesis                       
There is not enough evidence to conclude that true proportion is different from 0.17