Question

A gaming company claimed that their role-playing games take over 65 hours to complete. A sample of 300 gamers played their role-playing games and were able to complete them with a mean time of 63, hours with a standard deviation of 10 hours. Using a 1% level of significance, test the gaming company's hypothesis.

A. Reject the null hypothesis. There is enough evidence to oppose the gaming company's claim.
B. Reject the null hypothesis. There is not enough evidence to oppose the gaming company's claim.
C. Fail to reject the null hypothesis. There is not enough evidence to oppose the gaming company's claim.
D. Fail to reject the null hypothesis. There is enough evidence to oppose the gaming company's claim.

Answer 1

A) Reject the null hypothesis. There is enough evidence to oppose the gaming company's claim.

Explanation:

The test statistic needs to fall within the rejection regions that are above and below the critical z-score associated with a 1% level of significance in order to reject the null hypothesis. Otherwise, we will fail to reject the null hypothesis.

Answer 2

D. Fail to reject the null hypothesis. There is enough evidence to oppose the gaming company's claim.

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):

`\textsf{sample mean }\overline{x}=63,\quad \sigma=10, \quad n=300`

`\implies z=\frac{\overline{x}-\mu}{\sigma / √(n)}=(63-65)/(10 / √(300))=-2√(3)=-3.4641...`

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.