Use the t-distribution and the sample results to
complete the test of the hypotheses. Use a 5% significance level.
Assume the results come from a random sample, and if the sample
size is small, assume the underlying distribution is relatively
normal.
Test Ho : μ=120 vs Ha : μ<120 using the sample results x¯=112.3,
s=18.4, with n=100.
a) Give the test statistic and the p-value
Test statistic = _____
P-value = _____
Solution : -
Given that ,
= 120
= 112.3
s = 18.4
n = 100
This is the two tailed test .
The null and alternative hypothesis is ,
H0 : = 120
Ha : < 120
This is the left tailed test .
Test statistic = T
= ( - ) / s / n
= ( 112.3 - 120 ) / 18.4 / 100
= -4.18
The test statistic = -4.18
df = n - 1 = 100 - 1 = 99
P -value = ( t -4.18 , 99 ) = 0.0000
P-value = 0.0000
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