Question

The score of 24 randomly selected exams in a geometry class are given below:

72 85 62 88 75 65 76 99 74 67 83 50 98 78 90 70 80 55 78 77 70 80 68 60

It has been reported that the mean score of all geometry exams is less than 78. Test the validity of the report at α = 0.02 by using the data given above.

(a) Clearly, state H0 and H1, identify the claim and type of test.

H0 :

H1 :

b) Find and name all related critical values, draw the distribution, and clearly mark and shade the critical region(s).

(c) Find the computed test statistic and the P-value.

C.T.S. :

P-Value :

(d) Use non-statistical terminology to state your final conclusion about the claim.

It has also been reported that the standard deviation of all scores in a geometry exam is 10. Test the validity of the report at α = 0.01 by using the data given above.

(e) Clearly, state H0 and H1, identify the claim and type of test.

H0 :

H1 :

(f) Find and name all related critical values, draw the distribution, clearly mark and shade the critical region(s).

(g) Find the computed test statistic and the P-value.

C.T.S. :

P-Value :

(h) Use non-statistical terminology to state your final conclusion about the claim.

Answer 1

a)

Ho :   µ =   78
Ha :   µ <   78
b)

degree of freedom=   DF=n-1=   23

critical t value, t*   =   -2.177 [ excel function: =t.inv(0.02,23)

decision rule : cpmputed test statistics<t-critical value,reject Ho,other wise not

c)

Level of Significance ,    α =    0.02
sample std dev ,    s =    12.20833642
Sample Size ,   n =    24
Sample Mean,    x̅ =   75
Standard Error , SE =   s/√n =   2.4920
      
t-test statistic=   (x̅ - µ )/SE =    -1.2038
p-Value   =   0.1204
Conclusion:     p-value>α, Do not reject null hypothesis

d)

mean score of all geometry exams is not less than 78

e)

Ho :   σ =   10
Ha :   σ ╪   10
f)

degree of freedom,   DF=n-1 =    23

Two-Tail Test      
Lower Critical Value   =   9.260424776 [ excel function =CHISQ.INV.RT(1-α/2,df) ]
Upper Critical Value   =   44.18127525 [ excel function : =CHISQ.INV.RT(α/2,df)
decision rule : test statistics lies within this interval, do not reject Ho, otherwise reject Ho

g)

Level of Significance ,    α =    0.01
sample Std dev ,    s =    12.20833642
Sample Size ,   n =    24
      
Chi-Square Statistic,   X² = (n-1)s²/σ² =    34.28
p-Value   =   0.061216463
      
Do not reject the null hypothesis      

f)

standard deviation of all scores in a geometry exam is 10

--------------------------------------------------------