Question

**An alien empire came to Earth to brainwash people, the
aliens claimed they brainwashed half of the population. A random
sample of 500 people was selected, will a mean score of 245 being
brainwashed. The standard deviation of 80 and assuming .50 as the
alpha level. Are the alien’s claims correct?**

Answer #1

Claim is that

Null and alternate hypothesis for the claim are

Given values are

population mean mu = 250

sample mean xbar = 245, population standard deviation (sigma) = 80

sample size n = 500

Using z distribution to find the p value for z = -1.40, we get

p value = 0.1616 > significance level 0.05, so we failed to reject the null hypothesis

Therefore, at 0.05 significance level, we have sufficient
evidence to conclude that the **alien’s claims
correct**

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