A recent gasoline survey shows that the national average price of gasoline was $3.498 a gallon. It was felt that gasoline in Texas was significantly lower than the national average. A survey of 10 different suburbs in Dallas, Texas found the average price of gasoline to be $3.394 a gallon with a sample standard deviation of $0.1526. Assume that gas prices follow a normal distribution. We will perform a hypothesis test for this claim at α = 0.01.
The test statistic is:
Question 3 options:
1)
2.155
2)
3.121
3)
-2.155
4)
-3.121
The test statistic for this hypothesis test can be calculated as follows:
t = (x̄ - μ) / (s/√n)
Where:
x̄ = sample mean ($3.394)
μ = population mean ($3.498)
s = sample standard deviation ($0.1526)
n = sample size (10)
Plugging in the given values, we get:
t = (3.394 - 3.498) / (0.1526/√10)
= (-0.104) / (0.1526/√10)
Calculating this expression results in:
t ≈ -2.1547
Therefore, the correct answer is option 3) -2.155.