Question 1181285: A recent gasoline survey said that the national average price of gasoline was $1.498 a gallon It was felt that gasoline in Texas was significantly lower than the national averageA survey of 10 different suburbs in Dallas , Texas found the average price of gasoline to be a gallon with a standard deviation of $0.326. Find the p-value for this hypothesis test.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's how to find the p-value for this hypothesis test:
**1. State the Hypotheses:**
* Null Hypothesis (H0): The average price of gasoline in Texas is the same as the national average (μ = $1.498).
* Alternative Hypothesis (H1): The average price of gasoline in Texas is significantly lower than the national average (μ < $1.498). This is a left-tailed test.
**2. Significance Level:** While not explicitly stated, we'll proceed with a common significance level, such as α = 0.05, if needed for a conclusion later.
**3. Calculate the Test Statistic (t-score):**
Since the sample size is small (n = 10) and the population standard deviation is unknown, we use a t-test.
t = (sample mean - population mean) / (sample standard deviation / √sample size)
t = (1.25 - 1.498) / (0.326 / √10)
t = -0.248 / (0.326 / 3.162)
t ≈ -0.248 / 0.103
t ≈ -2.41
**4. Determine the Degrees of Freedom:**
Degrees of freedom (df) = n - 1 = 10 - 1 = 9
**5. Find the P-value:**
Because this is a left-tailed test, the p-value is the probability of getting a t-score as extreme as -2.41 or *lower*. Use a t-table or a statistical calculator to find this probability.
For a t-score of -2.41 and 9 degrees of freedom, the p-value is approximately 0.018.
**6. Conclusion (if α = 0.05):**
Since the p-value (0.018) is *less than* the significance level (0.05), we *reject* the null hypothesis.
**7. Conclusion Statement:**
There is sufficient evidence at the 0.05 significance level to conclude that the average price of gasoline in Texas is significantly lower than the national average.
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