Testing hypothesis: Null hypothesis

Question

I had an earlier question not satisfactorily answered and I am still smarting with ignorance. Please help with this question:

I can guess that the null hypothesis is: "Method 1 better for production". The alternate hypothesis is method II.

Answer 1

Let $X$ (a random variable) be a (random) outcome from Method 1 and $Y$ a random outcome from Method 2. The problem tells you

• You have an observed sample $X_1,\ldots,X_{64}$ which are independently and identically distributed (i.i.d.) as $X$. You are further told that the sample mean of $\{X_1,\ldots,X_{64}\}$ is $106$ and the sample standard deviation is $12$.
• Similarly, you also have $Y_1,\ldots,Y_{64}$ i.i.d. as $Y$ with $\{Y_1,\ldots,Y_{64}\}$ having sample mean $100$ and sample standard deviation $10$.

The null you are interested in is then: $$ H_0:E(X)\geq E(Y) $$ and the alternative $H_1:E(X)<E(Y)$.

So that should clarify the question for you. As for how to actually answer it, you can study up on the Welch $t$-tests.