(Round all intermediate calculations to at least 4 decimal places.) In order to
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(Round all intermediate calculations to at least 4 decimal places.) In order to conduct a hypothesis test for the population mean, a random sample of 24 observations is drawn from a normally distributed population. The resulting sample mean and sample standard deviation are calculated as 6.3 and 2.5, respectively. Use Table 2 Use the p-value approach to conduct the following tests at = 0.05. Ho: s 5.1 against HA: > 5.1 a-1. Calculate the value of the test statistic. (Round your answer to 2 decimal places.) Test s a-2. Approximate the p-value. 0 0.050Explanation / Answer
Given that,
population mean(u)=5.1
sample mean, x =6.3
standard deviation, s =2.5
number (n)=24
null, Ho: <=5.1
alternate, H1: >5.1
level of significance, = 0.05
from standard normal table,right tailed t /2 =1.714
since our test is right-tailed
reject Ho, if to > 1.714
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =6.3-5.1/(2.5/sqrt(24))
to =2.35
| to | =2.35
critical value
the value of |t | with n-1 = 23 d.f is 1.714
we got |to| =2.35 & | t | =1.714
make decision
hence value of | to | > | t | and here we reject Ho
p-value :right tail - Ha : ( p > 2.3515 ) = 0.01382
hence value of p0.05 > 0.01382,here we reject Ho
ANSWERS
---------------
null, Ho: <=5.1
alternate, H1: >5.1
a-1.
test statistic: 2.35
critical value: 1.714
a-2.
p-value: 0.01382
option:0.01<p<0.025
a-3.
decision: reject Ho since p value greater than alpha
b.
Given that,
population mean(u)=5.1
sample mean, x =6.3
standard deviation, s =2.5
number (n)=24
null, Ho: =5.1
alternate, H1: !=5.1
level of significance, = 0.05
from standard normal table, two tailed t /2 =2.069
since our test is two-tailed
reject Ho, if to < -2.069 OR if to > 2.069
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =6.3-5.1/(2.5/sqrt(24))
to =2.35
| to | =2.35
critical value
the value of |t | with n-1 = 23 d.f is 2.069
we got |to| =2.35 & | t | =2.069
make decision
hence value of | to | > | t | and here we reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != 2.3515 ) = 0.0276
hence value of p0.05 > 0.0276,here we reject Ho
ANSWERS
---------------
null, Ho: =5.1
alternate, H1: !=5.1
b-1.
test statistic: 2.35
critical value: -2.069 , 2.069
b-2.
p-value: 0.0276
option:
0.020 <p<0.050
b-3.
decision: reject Ho since p value less than alpha
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