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A survey of 32 different gas stations in Texas found the average price of gasoline to be $3.19 a gallon with a sample standard deviation of $0.096. Let μ be the true average price of gasoline price in Texas. The survey company claimed that gasoline in Texas was significantly lower than the national average $3.26 a gallon. The alernative hypothesis to test the claim is H 1 : μ <$3.26. Calculate the test statistic.

Respuesta :

Answer:

The value of test statistic is -4.1247

Step-by-step explanation:

We are given the following in the question:  

Population mean, μ = $3.26 a gallon

Sample mean, [tex]\bar{x}[/tex] = $3.19 a gallon

Sample size, n = 32

Sample standard deviation, σ = $0.096

First, we design the null and the alternate hypothesis

[tex]H_{0}: \mu = 3.26\text{ dollars a gallon}\\H_A: \mu < 3.26\text{ dollars a gallon}[/tex]

We use one-tailed t test to perform this hypothesis.

Formula:

[tex]t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }[/tex]

Putting all the values, we have

[tex]t_{stat} = \displaystyle\frac{3.19 - 3.26}{\frac{0.096}{\sqrt{32}} } = -4.1247[/tex]

Thus, the value of test statistic is -4.1247