according to the energy information administration (officially energy statics from the US Government) the mean price for one gallon of unleaded regular gas in the US cities for the year 2007 was 2.80 A random sample of 30 pumps in georgia yielded and average price of 284 per gallon for unleaded gasoline. assume that .90 is the standard deviation. test whether the population mean price for unleaded gas is higher in georgia than that of general population using significance level alpha=.01
Use same process as indicated on previous post.
To test whether the population mean price for unleaded gas is higher in Georgia than that of the general population, we can conduct a hypothesis test.
First, let's set up the hypothesis:
Null Hypothesis (H0): The population mean price for unleaded gas in Georgia is equal to or less than the general population mean.
Alternate Hypothesis (Ha): The population mean price for unleaded gas in Georgia is higher than the general population mean.
Next, we need to determine the critical value using the given significance level (alpha = 0.01). Since this is a one-sided test and we want to test whether the mean is higher, we will use the right-tailed test.
To find the critical value, we can use the t-distribution with degrees of freedom equal to the sample size minus 1 (n - 1). In this case, n = 30, so the degrees of freedom is 29.
Using a t-table or a t-distribution calculator with alpha = 0.01 and degrees of freedom = 29, the critical value for a one-sided test is approximately 2.462.
Now, we can calculate the test statistic.
The formula to calculate the t-test statistic is:
t = (sample mean - hypothesized population mean) / (sample standard deviation / sqrt(sample size))
Given:
Sample mean (x̄) = $2.84
Hypothesized population mean (μ0) = $2.80
Sample standard deviation (s) = $0.90
Sample size (n) = 30
Plugging in the values, we get:
t = (2.84 - 2.80) / (0.90 / sqrt(30))
= 0.04 / (0.90 / 5.477)
≈ 0.04 / 0.1638
≈ 0.244
Now, compare the calculated t-test statistic with the critical value.
If the calculated t-value is greater than the critical value, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.
In this case, the calculated t-value is 0.244, which is less than the critical value of 2.462. Therefore, we fail to reject the null hypothesis.
Based on the results of the hypothesis test, there is not enough evidence to conclude that the population mean price for unleaded gas in Georgia is higher than that of the general population at a significance level of 0.01.