a popular video game claims that the average time needed to reach level 10 paladin is 3 hours with a…
a popular video game claims that the average time needed to reach level 10 paladin is 3 hours with a standard deviation of 0.4 hours. james thinks that he and his four friends are more skilled than the average gamer because it took them an average of only 2.5 hours. which of the following is the most restrictive level that would validate his claim?\n\n| upper - tail values | | | |\n| ---- | ---- | ---- | ---- |\n| a | 5% | 2.5% | 1% |\n| critical z - values | 1.65 | 1.96 | 2.58 |\n\n1% \n2.5% \n5% \n10%
Answer
Explanation:
Step1: Calculate the z - score
The formula for the z - score in a sampling distribution of the mean is $z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}$. Here, $\mu = 3$ (population mean), $\bar{x}=2.5$ (sample mean), $\sigma = 0.4$ (population standard deviation), and $n = 5$ (sample size). So, $z=\frac{2.5 - 3}{\frac{0.4}{\sqrt{5}}}=\frac{- 0.5}{\frac{0.4}{\sqrt{5}}}\approx\frac{-0.5}{0.179}\approx - 2.79$. Since we are interested in validating that they are more skilled (i.e., took less time), we consider the absolute value of the z - score, $|z|\approx2.79$.
Step2: Compare with critical z - values
We compare the calculated z - value with the critical z - values in the table. The critical z - value for 1% upper - tail is 2.58, for 2.5% is 1.96, for 5% is 1.65. Our calculated $|z|\approx2.79$ is greater than 2.58.
Answer:
1%