Question

In a test of

Upper H 0H0​:

muμequals=100

against

Upper H Subscript aHa​:

muμnot equals≠​100,

the sample data yielded the test statistic

z equals 1.87z=1.87.

Find the

Upper PP​-value

for the test.

P equals=???

​(Round to four decimal places as​ needed.)

Answer 1

For testing,

vs

Given that test statistic is Z=1.87 and we also know that this Z follows N(0,1) distribution.

And we want to compute p-value of the test.

Here the test is two tailed test. And for two tailed Z-test p-value is given by the formula,

[ where, z = observe value of Z , for this problem z=1.87 ]

[ Since, if Z~N(0,1) then we get,   and for continuous distribution " less than "or " less than or equal to " are same ]

[ from standard normal probability table we get, ]

[round to four decimal places]

Answer:- p-value = 0.0615 [round to four decimal places]