The sample statistics are mean= 6.4, s = 10. In the test:
H0: μ = 10 H1: μ < 10 using α = .05. Which of the following statements do you KNOW is correct? A. A type 1 error has been committed. B. H0 is rejected. C. H0 is not rejected. D. Statements (A) and (B) are correct. E. None of the above.
Just super confused as to how to solve this
What is the probability that a normally distributed random variable with mean = 10 (the hypothesized mean) and standard deviation 10 (the observed sample deviation) would produce in 25 observations a mean of 6.4?
The observed mean is $(6.4-10) = -3.6$ away from expectations.
The deviation of the average over 25 samples is: $\frac {s}{\sqrt n} = \frac {10}{5} = 2$
$z = \frac {-3.6}{2} = 1.8$
What is $P(z\le -1.8)$?
We look it up on our standard normal table, or run it through our statistical calculator and get $P(z\le -1.8)\approx 3.8\%$ But, are we running a 1 tailed test or a two tailed test? Running a two tailed test, we would require $z < -2$ or $z > 2$ to reject the null hypothesis.