Question

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? upper-tail values a 5% 2.5% 1% critical z-values 1.65 1.96 2.58 1% 2.5% 5% 10%

Answer 1

The probability that the claim of James is correct is 1%.

What is a standard error?

The standard deviation of a statistic's sample distribution, or an approximation of that standard deviation, is its standard error. The standard error of the mean is the term used when the statistic is the sample mean.

In order to know if the claim of James is correct or not, firstly we need to determine the standard error. The standard error is the ratio of the standard deviation and the square root of the sample. Therefore, the standard error can be written as,

$\rm Standard\ Error, SE =\dfrac{\sigma}{\sqrt n} = \dfrac{0.4}{\sqrt5} =0.178$

Thus, the standard error is 0.178.

Further, The z-score is defined as the distance from the sample to the population mean in units of standard error. Therefore, the z-score can be written as,

$z = \dfrac{X-\mu}{SE}=\dfrac{(3- 2.5)}{0.178} = 2.81$

Using the Z-table in order to know the probability of the claim of James is correct or not, therefore, at this z-score, the probability is 0.9974≈1.00%.

Hence, the probability that the claim of James is correct is 1%.

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