An industrical researcher is a consulant to a large chain of bookstores. Indusrt
ID: 3230426 • Letter: A
Question
An industrical researcher is a consulant to a large chain of bookstores. Indusrtry reportd shpw that for bookstores in general the number of complaints recieved by management for 1 month period of time of the year is 6.5 (varience is unknown). Seven of the chain's are randomly selected to keep records of complaints recieved over a 1-month period. The complaint numbers are (4,8,9,0,3,5 and 6). Does this chain get a different amount of complains than book stores in general at 0.05 sinificant level? What type of statistal test is used to find this out and how would I do hyporthesis testing? Lastly is the effect size small (.20,) medium( .50) or large (.80)?
Explanation / Answer
Level of significance =0.05
Null hypothesis
Ho:µ =6.5
Alternative hypothesis
HA: µ1 6.5
two tailed sample t-test will be used , because standard deviation not given
degrees of freedom df=n-1 =7-1 =6
since /2 =0.025
critical values z/2 =2.447 (from the t value table at df=6 , /2 =0.025 )
z< -2.447 or z > 2.447
x
(x- x^bar)
(x-x^bar )2
4
-1
1
8
3
9
9
4
16
0
-5
25
3
-2
4
5
0
0
6
1
1
35
56
mean x^bar =x/ 2
=35 / 7 =5
standard deviation = sort( (x- x^bar )2) /(n-1)
=sqrt(56/6) =3.0551
teststatistic = (x^bar –) /(s/ sqrt(n)
=( 5-6.5) /3.0551 /sqrt(7)
= -1.2990
t does not lie the rejection area so fail to reject Ho
x
(x- x^bar)
(x-x^bar )2
4
-1
1
8
3
9
9
4
16
0
-5
25
3
-2
4
5
0
0
6
1
1
35
56