Question

According to a recent study annual per capita consumption of milk in the United States is 21.5 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
29.8
23.84
25.25
21
17.52
19.61
19.83
26.18
34.97
30.2
28.59
20.57
26.94
27.24

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: ? _________> 21.5≥ 21.5= 21.5≤ 21.5< 21.5≠ 21.5

   H_a: ? _________> 21.5≥ 21.5= 21.5≤ 21.5< 21.5≠ 21.5

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

   (2 decimals)

3. At ? = 0.05, test for a significant difference by completing the following.

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

   The p-value is  (4 decimals)

   Reject the null hypothesis?

   _____NoYes

   What is your conclusion?

Answer 1

	Values ( X )	Σ ( Xi- X̅ )2
	29.8	21.9961
	23.84	1.6129
	25.25	0.0196
	21	16.8921
	17.52	57.6081
	19.61	30.25
	19.83	27.8784
	26.18	1.1449
	34.97	97.2196
	30.2	25.9081
	28.59	12.1104
	20.57	20.6116
	26.9	3.3489
	27.24	4.5369
Total	351.54	321.1376

Mean X̅ = Σ Xi / n
X̅ = 351.54 / 14 = 25.11
Sample Standard deviation S_X = √ ( (Xi - X̅ )² / n - 1 )
S_X = √ ( 321.1376 / 14 -1 ) = 4.9702

Part a)

To Test :-

H0 :- µ = 21.5
H1 :- µ > 21.5

Part b)

Point estimate of the difference between mean annual consumption is 25.11 - 21.50 = 3.61

Part c)

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 25.11 - 21.5 ) / ( 4.9702 / √(14) )
t = 2.72

P - value = P ( t > 2.7177 ) = 0.0088
Looking for the value t = 2.72 in t table across n - 1 = 13 degree of freedom.

Decision based on P value
Reject null hypothesis if P value < α = 0.05 level of significance
P - value = 0.0088 < 0.05 ,hence we reject null hypothesis
Conclusion :- Reject null hypothesis

Conclusion :- There is sufficient evidence to support the claim that milk consumption is higher in midwest.