SOLUTION: The dean of a university estimates that the mean number of classroom hours per week for​ full-time faculty is 10.0. As a member of the student​ council, you want to tes
Algebra.Com
Question 982171: The dean of a university estimates that the mean number of classroom hours per week for full-time faculty is 10.0. As a member of the student council, you want to test this claim. A random sample of the number of classroom hours for 8 full-time faculty for one week is shown in the table below. At α=0.10 can you reject the dean's claim? Complete parts (a) through (c) below.
Assume the population is normally distributed.
10.3,8.2,11.3,6.5,4.9,9.6,14.1,8.8
A. write the claim mathematically
B. What is the P value?
C. Decide whether to reject or fail to reject the null hypothesis.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
A) The claim is mu = 10.0
The claim is the null hypothesis. The alternate hypothesis is mu =/= 10.0, so we have a two tailed test.
-----------------------------------------------------------------
B)
Use a calculator to find that
xbar = 9.2125
s = 2.84677
Now compute the test statistic:
t = (xbar - mu)/(s/sqrt(n))
t = (9.2125- 10)/(2.84677/sqrt(8))
t = -0.78
Use either a table or a calculator to find that P(T < -0.78) = 0.23047 (the degrees of freedom equals n-1 = 8-1 = 7)
The p-value is therefore 2*0.23047 = 0.46094
-------------------------------------------------------
C)
The p-value 0.46094 is larger than alpha = 0.10. So we fail to reject the null. We "accept" the claim that the mean mu is 10.0. We don't have enough evidence to overturn it.
RELATED QUESTIONS
The dean of a university estimates that the mean number of classroom hours per week for... (answered by Boreal)
The dean of a university estimates that the mean number of classroom hours per week for... (answered by ewatrrr)
The dean of a university estimates that the mean number of classroom hours per week... (answered by Boreal)
The London Enquirer, in its Sunday business supplement, reported that ... (answered by Theo)
The Cincinnati Enquirer, in its Sunday business supplement, reported that the mean number (answered by sojazzy80)
You receive a brochure from a large university. The brochure indicates that the mean... (answered by jim_thompson5910)
​Full-time college students report spending a mean of 25 hours per week on academic​... (answered by Theo)
the number of adjunct faculty at a community college is 206 more than the number of... (answered by stanbon)
You receive a brochure from a large university. The brochure indicates that the mean... (answered by stanbon)