Question

According to the Energy Information Administration (official energy statistics from the U.S. government), the mean price for one gallon of unleaded regular gasoline in U.S. cities for August, 2011 was $3.64. A random sample of 30 pumps in cities in the state of Georgia yielded an average price of $3.16 per gallon for unleaded gasoline. Assume that σ = $0.90. Test whether the population mean price for unleaded gasoline is lower in Georgia than the general population, using a significance level of α = 0.01.

Hint : Do you need to conduct a t-test or a z-test? Remember Q9 questions and you can eliminate half of the choices. Next, find p-value, Using p-value and level of significance, you can see if the decision (Reject or Do Not reject H₀.) You can also find the critical value(s) to finalize your decision.

Question 3 options:

1.	Zdata< Zcritical   and decision is Reject   H0.
2.	Zdata< Zcritical   and decision is Do NOT Reject   H0.
3.	Zdata> Zcritical   and decision is Do NOT Reject   H0.
4.	Zdata> Zcritical   and decision is to Reject   H0.
5.	tdata> tcritical and decision is Do NOT Reject   H0.
6.	tdata> tcritical and decision is to Reject   H0.
7.	tdata< tcritical     and decision is Do NOT Reject   H0.
8.	tdata< tcritical     and decision is to Reject   H0.
9.	tcritical <tdata< tcritical     and decision is Do NOT Reject   H0.
10.	tcritical <tdata< tcritical     and decision is to Reject   H0.
11.	zcritical <zdata< zcritical     and decision is Do NOT Reject   H0.
12.	zcritical <zdata< zcritical     and decision is to Reject   H0.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 3.64
Alternative Hypothesis, Ha: μ < 3.64

Rejection Region
This is left tailed test, for α = 0.01
Critical value of z is -2.33.
Hence reject H0 if z < -2.33

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (3.16 - 3.64)/(0.9/sqrt(30))
z = -2.92

P-value Approach
P-value = 0.0018
As P-value < 0.01, reject the null hypothesis.

  
Zdata< Zcritical and decision is Reject H0.