Question

Small Sample Mean Problem. Each year the Heritage Foundation creates an Index of Economic Freedom for countries around the word based on assessments of freedom on property rights, corruption, business freedom, and labor freedom, among many others. We have a sample of 31 countries taken from the 2016 data. The following is a summary of this sample. Economic Freedom STEM Leaf 4 4* 64 5 09 18 22 24 32 42 5*160 65 74 75 76 77 91 93 6 00 02 12 19 22 30 31 6* 59 66 75 87 7126 39 43 7* 54 77 Mean Median Min Max Variance Std Deviaton 61.174 60.000 46.400 77.700 63.004 7.938 12.975 CV Count 31 A value of 4164 is an index of 46.4 The Heritage Foundation feels an index below 60 reflects a country that is mostly unfree. If we were to conduct a test to see if the sample estimate is above 60 at an alpha level = . 10, what is the test statistic for this test? 01.310 1.697 0 -1.310 and 1.310 0.8235

Answer 1

Given that,
population mean(u)=60
sample mean, x =61.174
standard deviation, s =7.938
number (n)=31
null, Ho: μ=60
alternate, H1: μ>60
level of significance, α = 0.1
from standard normal table,right tailed t α/2 =1.31
since our test is right-tailed
reject Ho, if to > 1.31
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =61.174-60/(7.938/sqrt(31))
to =0.8235
| to | =0.8235
critical value
the value of |t α| with n-1 = 30 d.f is 1.31
we got |to| =0.8235 & | t α | =1.31
make decision
hence value of |to | < | t α | and here we do not reject Ho
p-value :right tail - Ha : ( p > 0.8235 ) = 0.20837
hence value of p0.1 < 0.20837,here we do not reject Ho
ANSWERS
---------------
null, Ho: μ=60
alternate, H1: μ>60
test statistic: 0.8235
critical value: 1.31
option:A
decision: do not reject Ho
p-value: 0.20837
we do not have enough evidence to support the claim that if sample estimate is above 60
3.
option:D
5.
type 1 error is not possible because fails to reject the null hypothesis.
option:B