H0: ƒÊX = ƒÊY
The mean (average) gas price in city X equals the mean (average) gas price in city Y during January 2012.
H1: ƒÊX �‚ ƒÊY
The mean (average) gas price in city X does not equal the mean (average) gas price in city Y during January 2012.
The given statements represent a hypothesis test. The null hypothesis (H0) states that the mean gas price in city X is equal to the mean gas price in city Y during January 2012. The alternative hypothesis (H1) states that the mean gas price in city X does not equal the mean gas price in city Y during January 2012.
To conduct a hypothesis test, you would typically collect a sample of gas prices from each city during January 2012. Then, you would calculate the sample means for each city. Next, you would perform a statistical test to determine if there is enough evidence to reject the null hypothesis and support the alternative hypothesis.
One commonly used test is the t-test. The t-test compares the means of two independent samples to determine if they are significantly different from each other. The test calculates a t-value, which is then compared to a critical value from the t-distribution. If the t-value is greater than the critical value, the null hypothesis can be rejected in favor of the alternative hypothesis.
To perform the t-test, you would need the sample means, the sample standard deviations, and the sample sizes for both cities. With this information, you can calculate the t-value using the formula:
t = (meanX - meanY) / sqrt((sX^2 / nX) + (sY^2 / nY))
Here, meanX and meanY are the sample means, sX and sY are the sample standard deviations, nX is the sample size for city X, and nY is the sample size for city Y. The t-value can then be compared to the critical value to determine the statistical significance.
Remember, hypothesis tests provide a way to make conclusions based on sample data. It is important to use the appropriate statistical test and consider factors such as sample size, significance level, and the assumptions of the test to ensure accurate results.