A sample of 40 observations is selected from a normal popula

A sample of 40 observations is selected from a normal population. The sample mean is 20, and the population standard deviation is 2. Conduct the following test of hypothesis using the 0.05 significance level.

H₁: >19

  Value of the test statistic

Solution

the test statistic is T=(Xbar-mu)*sqrt(n)/sigma

where Xbar=sample mean mu=population mean under H0   n=sample size sigma=population standard deviation

now Xbar=20 mu=19 n=40 sigma=2

c) so value of test statistic is T=(20-19)*sqrt(40)/2=3.1622 [answer]

e) now under H0 T~N(0,1)

so p-value is P[T>3.1622] where T~N(0,1)

using minitab p-value=0.000783 [answer]