Question

Can someone explain how this P-value is found step-by step?

Suppose that the sample
mean is x = 51.3, with n = 16 and st. dev = 2.5. Then we want to
find the smallest significance level so that 51.3 is outside the
acceptance region. In other words, since the symmetric
acceptance region is centered at the hypothesized the population mean (u) = 50, we
want the probability that the sample mean x is greater than
51.3 or less than 48.7, if the true population mean is = 50.

So we find P-value = 1 - P(48:7 < X < 51:3) = 0:038.

I am not sure how to evaluate the probability given the only info given was that the sample mean is 51.3

Answer 1

P value = 1 - P(48.7<X<51.3)

= .   

= 1 - P(-1.04<Z<0)

= 1 - [ P(Z<0) - P(Z<-1.04) ]

From Z table

= 1 - [ 0.5 - 0.1492 ]

= 0.6492

P value = 0.6492