(2 points) A random sample of 100 observations from a population with standard d

Question

(2 points) A random sample of 100 observations from a population with standard deviation 6.97 yielded a sample mean of 91.2 .

1. Given that the null hypothesis is =90 and the alternative hypothesis is >90 using =.05 , find the following:

(a) Test statistic =

(b) P - value:

(c) The conclusion for this test is:

A. There is insufficient evidence to reject the null hypothesis

B. Reject the null hypothesis

C. None of the above

2. Given that the null hypothesis is =90 and the alternative hypothesis is 90 using =.05 , find the following:

(a) Test statistic =

(b) P - value:

(c) The conclusion for this test is:

A. There is insufficient evidence to reject the null hypothesis

B. Reject the null hypothesis

C. None of the above

please show easy step by step and correct answers only

Explanation / Answer

Given that,
population mean(u)=90
standard deviation, =6.97
sample mean, x =91.2
number (n)=100
null, Ho: =90
alternate, H1: >90
level of significance, = 0.05
from standard normal table,right tailed z /2 =1.645
since our test is right-tailed
reject Ho, if zo > 1.645
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 91.2-90/(6.97/sqrt(100)
zo = 1.722
| zo | = 1.722
critical value
the value of |z | at los 5% is 1.645
we got |zo| =1.722 & | z | = 1.645
make decision
hence value of | zo | > | z | and here we reject Ho
p-value : right tail - ha : ( p > 1.722 ) = 0.043
hence value of p0.05 > 0.043, here we reject Ho
ANSWERS
---------------
null, Ho: =90
alternate, H1: >90
test statistic: 1.722
critical value: 1.645
decision: reject Ho
p-value: 0.043

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