Question

According to a recent study annual per capita consumption of milk in the United States is 22.6 gallons. Being from the Midwest, you believe milk consumption is higher there and wish to test your hypothesis. A sample of 14 individuals from the Midwestern town of Webster City was selected and then each person's milk consumption was entered into the Microsoft Excel Online file below. Use the data to set up your spreadsheet and test your hypothesis.

Gallons of Milk
28.3
23.84
25.25
21
17.52
19.61
19.83
26.18
34.97
30.1
28.59
20.57
26.94
27.24

Open spreadsheet

1. Develop a hypothesis test that can be used to determine whether the mean annual consumption in Webster City is higher than the national mean.

   H₀: ? _________> 22.6≥ 22.6= 22.6≤ 22.6< 22.6≠ 22.6

   H_a: ? _________> 22.6≥ 22.6= 22.6≤ 22.6< 22.6≠ 22.6

2. What is a point estimate of the difference between mean annual consumption in Webster City and the national mean?

   (2 decimals) ______

3. At ? = 0.01, test for a significant difference by completing the following.

   Calculate the value of the test statistic (2 decimals).

   _______

   The p-value is  (4 decimals)

4. Reject the null hypothesis?

   _____NoYes

   What is your conclusion?

   _________There is insufficient evidence to conclude that the population mean consumption of milk in Webster City is greater than the hypothesized mean.Conclude the population mean consumption of milk in Webster City is greater than the hypothesized mean.

Answer 1

a)

Ho :   µ =   22.6
Ha :   µ >   22.6

b)point estimate of the difference between mean annual consumption in Webster City and the national mean = 25.00-22.6 = 2.40

c)

sample std dev ,    s = √(Σ(X- x̅ )²/(n-1) ) =   4.8685                  
Sample Size ,   n =    14                  
Sample Mean,    x̅ = ΣX/n =    24.9957                  
                          
degree of freedom=   DF=n-1=   13                  
                          
Standard Error , SE = s/√n =   4.8685   / √    14   =   1.3012      
t-test statistic= (x̅ - µ )/SE = (   24.996   -   22.6   ) /    1.3012   =   1.84
                          
  
p-Value   =   0.0443 [Excel formula =t.dist(t-stat,df) ]              

d)

p-value>α, Do not reject null hypothesis   

answer: NO

There is insufficient evidence to conclude that the population mean consumption of milk in Webster City is greater than the hypothesized mean