Gaming company Vider believes their new gaming console has a longer battery life than the gaming console from competitor Metah. A small scale trial was held with 12 consoles from Vider and 15 from Metah. The results showed that the average battery life of the Vider console was 82.7 hours with a variance of 21.8 hours squared. For Metah, the average was 80.3 hours with a variance of 35.8 hours squared. It is assumed that the population variances are the same and the distribution of battery life for both groups closely approximates a normal distribution. Use an alpha of 0.05. 1. If the hypotheses are to be written in the form of the average of Vider minus the average of Metah, what is the direction of the alternative hypothesis used to test Vider's belief. Type the letters gt (greater than), ge (greater than or equal to), It (less than), le (less than or equal to) or ne (not equal to) as appropriate in the box. 2. Determine the standard error for the difference between means, reporting your answer to three decimal places. 3. Calculate the test statistic, reporting your answer to two decimal places. 4. Is the null hypothesis rejected for this test? Type yes or no. 5. Regardless of your answer for 4, if we fail to reject the null hypothesis, can we conclude that Vider's belief is valid at the 5% level of significance? Type yes or no.