Question

Given the following hypothesis test:
“It is believed that the mean amount of water per day that the Gondorans drink is L liters. A random sample of 36 Gondorans is observed. The average amount of water they drink per day is 1.62 liters, with a standard deviation of 0.4 liters. Is the mean amount of water that Gondorans drink less than L liters? Test with α = 0.025.”
What is the biggest possible value of L (rounded to two digits after the decimal point) so that the null hypothesis is still retained?
L = ___________________

Answer 1

Ho :   µ =   1.75                  
Ha :   µ <   1.75       (Left tail test)          
                          
Level of Significance ,    α =    0.03                  
sample std dev ,    s =    0.4000                  
Sample Size ,   n =    36                  
Sample Mean,    x̅ =   1.6200                  
                          
degree of freedom=   DF=n-1=   35                  
                          
Standard Error , SE = s/√n =   0.4000   / √    36   =   0.0667      
t-test statistic= (x̅ - µ )/SE = (   1.620   -   1.75   ) /    0.0667   =   -1.95
                          
critical t value, t* =        -2.0301   [Excel formula =t.inv(α/no. of tails,df) ]              
                          
p-Value   =   0.0296   [Excel formula =t.dist(t-stat,df) ]              
Decision:   p-value>α, Do not reject null hypothesis                       

L = 1.75

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