Test the claim about the population mean, mu, at the given level of significance

Question

Test the claim about the population mean, mu, at the given level of significance using the given sample statistics. Claim: mu = 40; alpha = 0.04; sigma = 3.51. Sample statistics: x = 38.7, n = 60 A. The critical values are plusminus B. The critical value is Determine the outcome and conclusion of the test. Choose the correct answer below. A. Fail to reject H_0. At the 4% significance level, there is not enough evidence to support the claim. B. Reject H_0. At the 4% significance level, there is enough evidence to support the claim. C. Fail to reject H_0. At the 4% significance level there is not enough evidence to reject the claim. D. Reject H_0. At the 4% significance level, there is enough evidence to reject the claim.

Explanation / Answer

Given that,
population mean(u)=40
standard deviation, =3.51
sample mean, x =38.7
number (n)=60
null, Ho: =40
alternate, H1: !=40
level of significance, = 0.04
from standard normal table, two tailed z /2 =2.054
since our test is two-tailed
reject Ho, if zo < -2.054 OR if zo > 2.054
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 38.7-40/(3.51/sqrt(60)
zo = -2.86888
| zo | = 2.86888
critical value
the value of |z | at los 4% is 2.054
we got |zo| =2.86888 & | z | = 2.054
make decision
hence value of | zo | > | z | and here we reject Ho
p-value : two tailed ( double the one tail ) - ha : ( p != -2.86888 ) = 0.00412
hence value of p0.04 > 0.00412, here we reject Ho
ANSWERS
---------------
null, Ho: =40
alternate, H1: !=40
test statistic: -2.86888
critical value: -2.054 , 2.054
decision: reject Ho
p-value: 0.00412

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