Question

Unlike most packaged food products, alcohol beverage containers are not required to show calorie or nutrition content. A random sample of 58 people was asked to estimate the calorie content of a 12-oz can of beer. The sample mean of their estimates was 191 calories and sample standard deviation was 89. The actual calorie content was 154 calories. Does this data suggest that the population average would overestimate the calories in this 12-oz can of beer? Carry out a 4-part hypothesis test(Hypotheses, assumptions, calculation and conclusion)at the significance level of α = .05. Show your work. For p-value use R code.

Answer 1

1)

Ho :   µ =   154                  
Ha :   µ >   154       (Right tail test)          
2)

sample are random and independent

and population is normally distibuted   
3)

Level of Significance ,    α =    0.05                  
sample std dev ,    s =    89.0000                  
Sample Size ,   n =    58                  
Sample Mean,    x̅ =   191.0000                  
                          
degree of freedom=   DF=n-1=   57                  
                          
Standard Error , SE = s/√n =   89.0000   / √    58   =   11.6863      
t-test statistic= (x̅ - µ )/SE = (   191.000   -   154   ) /    11.6863   =   3.166
                          
  
4)p-Value   =   0.0012  
Decision:   p-value<α, Reject null hypothesis