3. A fitness center is running a discounted membership fee. Did the discount increase the membership sales? Write your hypotheses mathematically.Write null and alternative hypothesis.
To determine whether the discount increased the membership sales at the fitness center, we can formulate the hypotheses mathematically.
Let's denote the original membership fee as μ and the discounted membership fee as x. The null hypothesis, denoted as H0, represents the assumption that the discount did not increase the membership sales. Conversely, the alternative hypothesis, denoted as Ha, represents the assumption that the discount did increase the membership sales.
Mathematically, we can state the hypotheses as follows:
Null hypothesis (H0): μ = x
Alternative hypothesis (Ha): μ < x
In this case, we are considering a one-tailed test because we are interested in whether the discount increased the membership sales, which implies the alternative hypothesis being μ < x.
To statistically test these hypotheses and draw a conclusion, we would need to collect data on membership sales with the original membership fee and with the discounted fee. We could then perform a hypothesis test, such as a t-test or a z-test, to determine if there is evidence to reject the null hypothesis in favor of the alternative hypothesis.