I am doing an exercise on marketing analysis to determine the strategy that a brand should follow based on historical weekly data collected from supermarkets that sell the brand (let say brand1) and 4 other competitors' products (brand2, 3, 4 and 5 respectively). The weekly data contains sales, average price ... of each brand by period, week and store number.
I want to analyse that whether brand 3 is doing better than our brand (brand 1) on average weekly sales. I am thinking about the two sample student's t-test. $H_0$ would be $\mu_3 - \mu_1 \ge 0$ and $H_1$ would be $\mu_3 - \mu_1 < 0$. ($\mu_3, \mu_1$ are the mean of weekly sales of brand 3 and brand 1 respectively).
Firstly, using a Fisher’s F-test to verify the homogeneity of variances. If the p-value is less than the significance level or if the F-value is less than the tabulated F-value, then we accept the null hypothesis of homogeneity of variances.
Secondly, implement the t-test for homogeneous variances. But I don't know what to do in case the null hypothesis $H_0$ is $\mu_3 - \mu_1 \ge 0$ (instead of $\mu_3 - \mu_1 = 0$).
Could anyone please help me on this case? Is there any other test more suitable to perform on this problem and if two sample t-test is applicable for the situation, what I need to do since the null hypothesis is $\mu_3 - \mu_1 \ge 0$ ?
Thank you so much in advance!