Many studies have been conducted to test the effects of marijuana use on mental abilities. In one such​ study, groups of light and heavy users of marijuana in college were tested for memory​ recall, with the results given below. Use a a 0.05 significance level to test the claim that in the population of heavy marijuana​ users, the mean number of items sorted correctly is lower than the mean number in the population of light users.   Items so

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Many studies have been conducted to test the effects of marijuana use on mental abilities. In one such​ study, groups of light and heavy users of marijuana in college were tested for memory​ recall, with the results given below. Use a a 0.05 significance level to test the claim that in the population of heavy marijuana​ users, the mean number of items sorted correctly is lower than the mean number in the population of light users.
 
Items sorted correctly by light marijuan​ users: n​ = 64,
x overbar equals

53.5

​,
s​ = 3.6
Items sorted correctly by heavy marijuan​ users: n​ = 65,
x overbar equals

51.8

​,
s​ = 4.5
a. Define the parameters
 
 
A.
mu 1 equals
 
The mean number of light marijuana users
mu 2 equals
 
The mean number of heavy marijuan users
 
B.
p 1 equals
 
The proportion of light marijuana users
p 2 equals
 
The proportion of heavy marijuana users
 
C.
p 1 equals
 
The proportion of items sorted correctly by all light marijuana users
p 2 equals
 
The proportion of items sorted correctly by all heavy marijuana users
 
D.
mu 1 equals
 
The mean number of items sorted correctly by all light marijuana users
mu 2 equals
 
The mean number of items sorted correctly by all heavy marijuana users
 
b. State the null and alternative hypotheses
 
 
A.
Upper H 0 : mu 1 equals mu 2 Upper H 1 : mu 1 greater than mu 2
 
 
B.
Upper H 0 : mu 1 equals

53.5

  
Upper H 1 : mu 2 equals

51.8

 
 
C.
Upper H 0 : p 1 equals p 2 Upper H 1 : p 1 greater than p 2
 
 
D.
Upper H 0 : mu 1 equals mu 2 Upper H 1 : mu 1 less than mu 2
 
 
c. Calculate the​ P-value. Which of these options is closest to its​ value?
 
 
A.
0.0088
 
 
B.
0.0110
 
 
C.
0.0132
 
 
D.
0.0096
 
 
d. State the technical conclusion
 
 
A.
Reject Upper H 0
 
 
B.
Do not reject Upper H 0
 
 
e. State the final conclusion
 
 
A.
The sample data support the claim.
 
B.
There is not sufficient evidence to warrant rejection of the claim.
 
C.
There is sufficient evidence to warrant rejection of the claim.
 
D.
There is not sufficient sample evidence to support the claim.
 
f. Should marijuana use be of concern to​ students?
 
 
A.
No
 
B.
Yes
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