Question

Questions 2 and 3 refer to the following information regarding the annual consumption of coffee of the 41 males. Of the sample of the 41 males, the sample mean is 25.7 gallons and the sample standard deviation is 3.8 gallons. Assume the data is normally distributed and the sample is randomly selected.

2. Assuming α = 0.005, is there enough evidence to support a claim that the mean amount of consumption is at least 28 gallons? (12 points)

3. Assuming α = 0.05, is there enough evidence to support a claim that the standard deviation of the number of servings is 3 gallons? (12 points)

4. For the entire random sample of 92 people, the sample mean is 21.6 gallons. Assume the population standard deviation is 4.8 gallons and that the population is normally distributed. Is there enough evidence to support a claim that the mean amount of consumption is more than 20.2 gallons? Assume α = 0.03. (12 points)

5. Of the 92 people in the sample, the annual consumption of coffee and the weekly amount of hours worked were compared to find r = 0.623. Test the significance of this correlation coefficient using α = 0.10. Is there a significant correlation between annual coffee consumption and the weekly amount of hours worked? (12 points)

Answer 1

2)

Ho :   µ =   28                  
Ha :   µ <   28       (Left tail test)          
                          
Level of Significance ,    α =    0.005   
sample std dev ,    s =    3.8000                  
Sample Size ,   n =    41                  
Sample Mean,    x̅ =   25.7000                  
                          
degree of freedom=   DF=n-1=   40                  
                          
Standard Error , SE = s/√n =   3.8000   / √    41   =   0.5935      
t-test statistic= (x̅ - µ )/SE = (   25.700   -   28   ) /    0.593   =   -3.8756
                          
  
p-Value   =   0.0001930 [Excel formula =t.dist(t-stat,df) ]              
Decision:   p-value<α, Reject null hypothesis

                      
there is enough evidence to reject the claim that the mean amount of consumption is at least 28 gallons at α=0.005

3)

Ho :   σ =   3
Ha :   σ ╪   3
      
Level of Significance ,    α =    0.05
sample Std dev ,    s =    3.8
Sample Size ,   n =    41
      
Chi-Square Statistic,   X² = (n-1)s²/σ² =    64.178
      
degree of freedom,   DF=n-1 =    40
p-Value   =   0.009

p value <α=0.05,

Reject the null hypothesis      
there enough evidence to reject  the claim that the standard deviation of the number of servings is 3 gallons