Question

​If, in a sample of nequals20 selected from a normal​ population, Upper X overbar equals 57 and Upper S equals 12​, what is your statistical decision if the level of​ significance, alpha​, is 0.05​, the null​ hypothesis, Upper H 0​, is mu equals 50 comma and the alternative​ hypothesis, Upper H 1 comma is mu not equals 50 question mark
Click here to view page 1 of the table of the critical values of t.LOADING... Click here to view page 2 of the table of the critical values of t.LOADING...
Determine the critical​ value(s).
The critical​ value(s) is(are)
nothing.
​(Round to four decimal places as needed. Use a comma to separate answers as​ needed.)

Determine the test statistic tSTAT ​(Round to four decimal places as needed)

Answer 1

Solution,

The null and alternative hypothesis is ,

H0 :   = 50

Ha :    50

= 57

s = 12

n = 20

degrees of frredom = n - 1 = 20 - 1 = 19

This is the two tailed test

= 0.05

/2 = 0.025

t/2,df = t0.025,19 = 2.0930

critical value = -2.0930, 2.0930

Test statistic = t =

= ( - ) / s / n

= (57 - 50) / 12 / 20

Test statistic = t = 2.6087