the null hypothesis is 𝜇=90 and the alternative hypothesis is 𝜇≠90 using 𝛼=.05, find the following: (a) Test statistic: (b) P - value:

Question

A random sample of 100 observations from a population with standard deviation 10.26 yielded a sample mean of 91.8.

the null hypothesis is 𝜇=90 and the alternative hypothesis is 𝜇≠90  using 𝛼=.05, find the following:

(a) Test statistic:

(b) P - value:

Answer 1

test statistic z = (sample mean - population mean)/(population standard deviation/square root(sample size))

You are given sample mean = 91.8, population mean = 90, population standard deviation = 10.26 and sample size = 100.

p-value is P(z > computed value) + P(z < - computed value) = 2*P(z < -computed value), which you can look up from standard normal probability table or using a statistical calculator or Excel.