Question

Problem 6 (20 Points) One-Sample Hypothesis Nancy believes that the average running time of movies is equal to 140 minutes. A

Answer 1

a)

it is two tail test

Ho :   µ =   140
Ha :   µ ╪   140

b)

sample std dev ,    s = √(Σ(X- x̅ )²/(n-1) ) =   15.0000                  
Sample Size ,   n =    4                  
Sample Mean,    x̅ = ΣX/n =    162.5000                  
                          
degree of freedom=   DF=n-1=   3                  
                          
Standard Error , SE = s/√n =   15.0000   / √    4   =   7.5000      
t-test statistic= (x̅ - µ )/SE = (   162.500   -   140   ) /    7.500   =   3

c)

critical t value, t* =    ±   2.3534   [Excel formula =t.inv(α/no. of tails,df) ]

d)

p-Value   =   0.0577   [Excel formula =t.dist(t-stat,df) ]

e)

Decision:   p-value<α, Reject null hypothesis

f)   
since, null hypothesis is rejected , Type II error could not be committed.