Use the following information to answer Questions 26-27 A random sample of size
ID: 3319237 • Letter: U
Question
Use the following information to answer Questions 26-27 A random sample of size 10 drawn from a normal population yielded the following results: x = 102, s-5. Perform the test, Ho: = 100 vs. Ha: 100 at = 0.05. 26. Compute the value of the test statistic. a. 2.83 c. Unknown, the information provided is not enough d. -2.83 e. 1.26 27. Which of the following is the correct decision regarding the null hypothesis using the critical value approach? a. The decision is to reject Ho because the test statistic falls in the rejection region [2.262, b. The decision is not to reject Ho because the test statistic does not fall in the rejection region (-,-2.262] U [2.262, oo) The decision is not to reject Ho because the test statistic does not fall in the rejection region [ 1.833, 00) c. d. Unknown, the information provided is not enough e. The decision is to reject Ho because the test statistic falls in the rejection region (-o0,- 1.96] U [1.96, 0)Explanation / Answer
Q.26
Given that,
population mean(u)=100
sample mean, x =102
standard deviation, s =5
number (n)=10
null, Ho: =100
alternate, H1: !=100
level of significance, = 0.05
from standard normal table, two tailed t /2 =2.262
since our test is two-tailed
reject Ho, if to < -2.262 OR if to > 2.262
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =102-100/(5/sqrt(10))
to =1.2649
| to | =1.2649
critical value
the value of |t | with n-1 = 9 d.f is 2.262
we got |to| =1.2649 & | t | =2.262
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != 1.2649 ) = 0.2377
hence value of p0.05 < 0.2377,here we do not reject Ho
ANSWERS
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null, Ho: =100
alternate, H1: !=100
critical value: -2.262 , 2.262
decision: do not reject Ho
p-value: 0.2377
OPTION: e(test statistic: 1.2649)
Q27.
hence value of p0.05 < 0.2377,here we do not reject Ho