3. You are testing Ho: =10 against Ha: >10 based on a SRS of 20 observations fro

Question

3. You are testing Ho: =10 against Ha: >10 based on a SRS of 20 observations from a Normal population. The data give x =12 and s=4 (i.e., the population standard deviation is unknown)

a). The value of test statistic is __________________________

b). The degree of freedom for this statistic is _______________

c). Estimating from the T table, the pvalue for the statistic is __________________

d). We use the t method in this problem. Because the t method is robust, the most important condition for its safe use is that _____

-A) the population standard deviation is known. B) the population distribution must be exactly Normal. C) the data can be regarded as an SRS from the population.

Explanation / Answer

3.

Given that,
population mean(u)=10
sample mean, x =12
standard deviation, s =4
number (n)=20
null, Ho: =10
alternate, H1: >10
level of significance, = 0.05
from standard normal table,right tailed t /2 =1.729
since our test is right-tailed
reject Ho, if to > 1.729
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =12-10/(4/sqrt(20))
to =2.236
| to | =2.236
critical value
the value of |t | with n-1 = 19 d.f is 1.729
we got |to| =2.236 & | t | =1.729
make decision
hence value of | to | > | t | and here we reject Ho
p-value :right tail - Ha : ( p > 2.2361 ) = 0.01877
hence value of p0.05 > 0.01877,here we reject Ho
ANSWERS
---------------
null, Ho: =10
alternate, H1: >10
test statistic: 2.236
critical value: 1.729
decision: reject Ho
degree of freedom = n-1=10-1=9
p-value: 0.01877
we have enough evidence to support the claim

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