Answer:
D. Fail to reject the null hypothesis. There is enough evidence to oppose the gaming company's claim.
Step-by-step explanation:
Let μ = mean time to complete a role-playing game.
The company claims that their role-playing games take over 65 hours to complete, so the hypotheses are:
H₀: μ = 65 H₁: μ > 65
Therefore, this is a one-tailed test.
The significance level is 1%, so α = 0.01.
Find the value of the test statistic (z):
[tex]\textsf{sample mean }\overline{x}=63,\quad \sigma=10, \quad n=300[/tex]
[tex]\implies z=\dfrac{\overline{x}-\mu}{\sigma / \sqrt{n}}=\dfrac{63-65}{10 / \sqrt{300}}=-2\sqrt{3}=-3.4641...[/tex]
Using the “Percentage Points of The Normal Distribution” table, the critical value is z = 2.3263 meaning the critical region is Z > 2.3263.
Since z = -3.4641... < 2.3263, the observed value of the test statistic lies outside the critical region. Therefore, the result is not significant.
Conclusion
There is sufficient evidence at the 1% level of significance to fail to reject H₀ and to oppose the alternative hypothesis that the mean time to complete the role-playing game is more than 65 hours.
