Consider the following hypothesis test: H 0 : 26 H a : > 26 A sample of 50 provi

Question

Consider the following hypothesis test:

H0: 26
Ha: > 26

A sample of 50 provided a sample mean of 27.4. The population standard deviation is 5.

a. Compute the value of the test statistic (to 2 decimals).

b. What is the p-value (to 4 decimals)?

c. At = .01, what is your conclusion?

p-value is Selectgreater than or equal to 0.01, rejectgreater than 0.01, do not rejectless than or equal to 0.01, do not rejectless than 0.01, rejectequal to 0.01, do not rejectnot equal to 0.01, do not rejectItem 3 H0

d. What is the rejection rule using the critical value?

Reject H0 if z is Selectgreater than or equal to 2.33greater than 2.33less than or equal to 2.33less than 2.33equal to 2.33not equal to 2.33Item 4

What is your conclusion?
SelectThe test statistic is greater than or equal to the critical value. Do not reject.The test statistic is less than the critical value. Reject.The test statistic is greater than the critical value. Do not reject.The test statistic is less than the critical value. Do not reject.The test statistic is equal to the critical value. Reject.The test statistic is not equal to the critical value. Do not reject.Item 5 H0

Explanation / Answer

Given that,
population mean(u)=26
standard deviation, =5
sample mean, x =27.4
number (n)=50
null, Ho: <=26
alternate, H1: >26
level of significance, = 0.01
from standard normal table,right tailed z /2 =2.326
since our test is right-tailed
reject Ho, if zo > 2.326
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 27.4-26/(5/sqrt(50)
zo = 1.9799
| zo | = 1.9799
critical value
the value of |z | at los 1% is 2.326
we got |zo| =1.9799 & | z | = 2.326
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value : right tail - ha : ( p > 1.9799 ) = 0.02386
hence value of p0.01 < 0.02386, here we do not reject Ho
ANSWERS
---------------
null, Ho: <=26
alternate, H1: >26
test statistic: 1.9799
critical value: 2.326
decision: do not reject Ho
p-value: 0.02386

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.