Question

The United States Department of Agriculture (USDA) claims that the national average price for one gallon of whole milk is $3.49, and that the population standard deviation is $0.64. You believe that the USDA’s claim is not correct, so you select a simple random sample of 35 grocery stores nationwide and record the price of a gallon of whole milk. Your sample mean price for a gallon of whole milk was $3.27. Using a significance level of .05, does it appear that the USDA’s claim is correct? Conduct a complete and appropriate hypothesis test.

Step 1 (Hypotheses)

H₀:    (Click to select)   σ   s   n   p   π   μ   x-bar      (Click to select)   =   ≠   ≤   >   ≥   <    

H_A:    (Click to select)   μ   x-bar   π   p   σ   s   n      (Click to select)   =   ≠   ≤   >   ≥   <    

Step 2 (Decision rule)

Using only the appropriate statistical table in your textbook, the critical value for rejecting H₀ is   (Click to select)   +   -   ±   . (report your answer to 2 decimal places, using conventional rounding rules)

Step 3 (Test statistic)

Using the sample data, the calculated value of the test statistic is   (Click to select)   +   -   ±   . (report your answer to 2 decimal places, using conventional rounding rules)

Step 4 (Evaluate the null hypothesis)

Should the null hypothesis be rejected?    (Click to select)   yes   no    

Step 5 (Practical conclusion)

Should you conclude that the national average price for one gallon of whole milk is $3.49?   (Click to select)   yes   no    

Using only the appropriate statistical table in your textbook, what is the p-value of this hypothesis test?   

Answer:  

Answer 1

Solution:

Given: The United States Department of Agriculture (USDA) claims that the national average price for one gallon of whole milk is $3.49, and that the population standard deviation is $0.64.

Sample size = n = 35

Sample mean =  

Level of significance = 0.05

Step 1 (Hypotheses)

H₀:   μ = 3.49

H_A:  μ  ≠ 3.49

Step 2 (Decision rule)

Level of significance = 0.05

Since this is two tailed, we find : Area =

Look in z table for area = 0.0250 or its closest area and find z value

Area 0.0250 corresponds to -1.9 and 0.06

thus z critical value = -1.96

Since this is two tailed test, we have two z critical values: ( -1.96 , 1.96)

that is:

the critical value for rejecting H₀ is ± 1.96

Step 3 (Test statistic)

Step 4 (Evaluate the null hypothesis)

Should the null hypothesis be rejected?

Since z test statistic value = < z critical value = -1.96, we reject null hypothesis H₀.

Thus correct answer is: Yes.

Step 5 (Practical conclusion)

Should you conclude that the national average price for one gallon of whole milk is $3.49?

Since we have rejected null hypothesis H₀:   μ = 3.49, we should not conclude that the national average price for one gallon of whole milk is $3.49.

Thus correct answer is: No.

what is the p-value of this hypothesis test?   

For two tailed test , p-value is:

p-value = 2* P(Z > z test statistic) if z is positive

p-value = 2* P(Z < z test statistic) if z is negative

thus

p-value = 2* P(Z < z test statistic)

p-value = 2* P(Z < -2.03)

Look in z table for z = -2.0 and 0.03 and find corresponding area.

P( Z< -2.03 ) = 0.0212

thus

p-value = 2* P(Z < -2.03)

p-value = 2* 0.0212

p-value = 0.0424