Respuesta :
In this case, it is equal to 0.178. The z-score is defined the distance from the sample to the population means in units of standard error. z = (3 – 2.5)/0.178 = 2.81 at this z-score, the probability is 0.9974 so A=1%
Using t-test for single mean, we find that the most restrictive level that would validate James' claim is 1%.
What is t - test?
The single sample t method tests a null hypothesis that the population mean is equal to a specified value.
The test statistic is calculated as:
[tex]t = \frac{x - mean }{standard\ deviation / \sqrt{sample\ size} }[/tex]
Given -
H0: average time needed to reach level 10 Paladin is 3 hours. (μ = 3)
H1: average time needed to reach level 10 Paladin is 2.5 hours. (μ < 3) (left tailed)
mean = 3 hours
standard deviation = 0.4 hours
sample size = 5
x = 2.5 hours
[tex]t = \frac{2-5 - 3}{0.4/\sqrt{5} } = \frac{-0.5}{1.79} = -0.28[/tex]
with (n - 1) 5 - 1 = 4 degree of freedom.
The most restrictive level that would validate his claim is that tabulated t value at [tex]\alpha[/tex] level of significance that is more than calculated |t|, i.e., the level of significance at which null hypothesis is rejected.
t(0.01, 4) = 3.74
t(0.025, 4) = 2.77
t(0.05, 4) = 2.13
t(0.1, 4) = 1.53
As can be observed, all level of significance validate James' claim. The most restrictive level would be the minimum level, which is 1%.
Learn more about t - test here
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