Question

We want to use this information to determine if there is an effect of friendship. In other words, is the mean price when buying from a friend the same as (or different from) the mean price when buying from a stranger? Assume the two groups have the same population standard deviation, and use significance level 0.05. Suppose that mu1 is the true mean price when buying from a friend and mu2 is the true mean price when buying from a stranger. (a) What are the null and alternative hypotheses?

Answer 1

H0 : mu1 = mu2

Ha : mu1 ≠ mu2

Which means

Null hypothesis H0; the true mean price when buying from a friend mu1 and the true mean price when buying from a stranger mu2 is the same/equal

Alternative hypothesis Ha; the true mean price when buying from a friend mu1 and the true mean price when buying from a stranger mu2 is different (not equal)

Explanation:

The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean(i.e it tries to prove that the old theory is true). While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.

Therefore, for the case above;

H0 : mu1 = mu2

Ha : mu1 ≠ mu2

Which means

Null hypothesis H0; the true mean price when buying from a friend mu1 and the true mean price when buying from a stranger mu2 is the same/equal

Alternative hypothesis Ha; the true mean price when buying from a friend mu1 and the true mean price when buying from a stranger mu2 is different (not equal)