Question

Home Videos Inc. surveys 450 households and finds that the mean amount spent for renting or buying videos is P135 a month and the standard deviation of the sample is P75.25. Is this evidence sufficient to conclude that the mean amount spent is greater than P127.50 per month at a 0.05 level of significance?

Answer 1

SOLUTION:

Case: Hypothesis testing

Step 1: Null and Alternative hypotheses

$\begin{gathered} H_0:\mu=P127.50 \\ H_1:\mu\leq P127.50 \end{gathered}$

Step 2: T-test analysis

$\begin{gathered} t=\frac{\hat{x}-\mu}{\frac{s}{\sqrt{n}}} \\ t=\frac{135-127.5}{\frac{75.25}{\sqrt{450}}} \\ t=2.144 \end{gathered}$

Step 3: t-test with the significance level

$\begin{gathered} t_{\alpha}=? \\ \alpha=0.05 \\ From\text{ }tables \\ t_{0.05}=1.654 \end{gathered}$

Step 4: Comparing

$t>t_{\alpha}$

So tail to reject the null hypothesis. There is enough evidence at a 0.05 level of significance to claim that the mean spent is greater than P127.50.

Final answer:

Yes, there is evidence sufficient to conclude that the mean amount spent is greater than P127.50 per month at a 0.05 level of significance.