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ELEMENTARYSTATISTICS
QUIZ NO. 5 / GROUP ACTIVITY
GROUP NAME:__________________________________
MEMBERS: ____________________________
____________________________
____________________________
____________________________
____________________________
SECTION: _________ DATE: ________
SCORE: _____________
1. A businessman is planning to open a new branch of coffee house in a village if the average income of an individual
living in the village is greater than P30, 000. In a random sample of 20 individuals, the following are their monthly income
in thousand pesos.
35 28 32.5 28.5 29 30 27.5 25 28 32
33 34 35 30 32 26.5 28.5 20 27 36
x́=29.875 s=3.91
Will he put up a new coffee house in the village? Use a 0.025 level of significance.
1 or 2 sample: 1 sample
z or t –test: t-test
1-Tailed (left/right) or 2-Tailed non-directional: 1-tailed (right)
Step I : Formulation of Ho and Ha
Ho: The average income of an individual living in the village is less than or equal to P30, 000.
Ha: The average income of an individual living in the village is greater P30, 000.
Step II: Level of Significance & Critical Value
α = 0.025; df = n – 1 = 20 – 1 = 19; critical value = 2.093
Step III: Test Statistics
x́−μ
t=
s
√n
29.875−30
t=
3.91
√ 20
t=−0.1429
Step IV: Decision
Since the computed t-value of -0.1429 is less than the critical t-value of 2.093, we accept the null hypothesis. The average
income of an individual living in the village is less than or equal P30, 000.
Step V: Conclusion
The businessman should not put up a new coffee house in the village.
2. The owner of an ice cream station wants to study the ice cream consumption of costumers at his ice cream station. A
random sample of 60 customers during a certain day is selected with a sample mean ice cream consumption of 11.3
grams with a standard deviation of 3.1 grams. At the 0.05 level significance, is there evidence that the mean consumption
is different from 10 grams?
z or t –test: z-test
1-Tailed (left/right) or 2-Tailed non-directional: 2-tailed test
Ho: The mean ice cream consumption is 10 grams.

Ha: The mean ice cream consumption is not equal to 10 grams.
α = 0.05; df = n – 1 = 60 – 1 = 59; critical value = ±1.96
x́−μ
z=
σ
√n
11.3−10
z=
3.1
√60
z=3.25
Step IV: Decision
Since the computed z-value of 3.35 is greater than the critical t-value of 1.96, we reject the null hypothesis. The mean ice
cream consumption is not equal to 10 grams.
Step V: Conclusion
The ice cream consumption of costumers at an ice cream station is different from 10 grams.
3.) The dealer of sedan cars claims that the new car model gets an average of 49 mpg. A buyer suspects that the dealer
is overrating the mileage of these cars. To test the truth of the claim, 8 units were driven and showed. Use 0.01 level of
significance.
48.7 49.2 47.0 48.0 45.8 46.9 49.0 49.6mpg

x́=48.025 s=1.34
z or t –test: t-test
1-Tailed (left/right) or 2-Tailed non-directional: 2-tailed
Step I: Formulation of Ho and Ha
Ho: The new car model gets an average of 49 mpg

Ha: The new car model gets an average not equal 49 mpg
α = 0.01; df = n – 1 = 8 – 1 = 7; critical value = 2.998
x́−μ
t=
s
√n
48.025−49
t=
1.34
√8
t=−2.06
Step IV: Decision
Since the computed t-value of -2.06 is less than the critical t-value of 2.998, we accept the null hypothesis. The new car
model gets an average of 49 mpg
Step V: Conclusion
The dealer is not overrating the mileage of the cars.

4. Past records show that the average final examination grade of students in Statistics is 66.6 with a standard deviation of
5.5. Two samples were taken, one from the BSBA-BM students of size 100 and another from the BSBA-MM students of
size 90. The mean final grade of the BSBA-BM students was 65.25 and that of the BSBA-MM was 67.0. Is there an
indication that the BSBA-MM students did better in the Statistics final examination? Test at α=0.01.
z or t –test z-test
1-Tailed (left/right) or 2-Tailed non-directional: 1-tailed
______________________
Ho: The mean final examination grade of BSBA-MM students is equal to the mean final examination grade of BSBA-BM.
Ha: The mean final examination grade of BSBA-MM students is greater than the mean final examination grade of BSBA-
BM.
α = 0.01; critical value = 2.33
x´1− x́ 2
z=
σ 2 σ2
√ +
n1 n 2
z=2.19
Step IV: Decision
Since the computed z-value of 2.19 is less than the critical t-value of 2.33, we accept the null hypothesis. The mean final
examination grade of BSBA-MM students is equal to the mean final examination grade of BSBA-BM.
Step V: Conclusion
There is no indication that the BSBA-MM students did better in the Statistics final examination.

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ELEMENTARYSTATISTICS

QUIZ NO. 5 / GROUP ACTIVITY

35 28 32.5 28.5 29 30 27.5 25 28 32

Step I : Formulation of Ho and Ha

Step II: Level of Significance & Critical Value

α = 0.025; df = n – 1 = 20 – 1 = 19; critical value = 2.093

Step III: Test Statistics

Step IV: Decision

Step I : Formulation of Ho and Ha

Ho: The mean ice cream consumption is 10 grams.

Step II: Level of Significance & Critical Value

α = 0.05; df = n – 1 = 60 – 1 = 59; critical value = ±1.96

Step III: Test Statistics

Step IV: Decision

48.7 49.2 47.0 48.0 45.8 46.9 49.0 49.6mpg

Step I: Formulation of Ho and Ha

Ho: The new car model gets an average of 49 mpg

Step II: Level of Significance & Critical Value

α = 0.01; df = n – 1 = 8 – 1 = 7; critical value = 2.998

Step III: Test Statistics

Step IV: Decision

The dealer is not overrating the mileage of the cars.

Step I : Formulation of Ho and Ha

Step II: Level of Significance & Critical Value

α = 0.01; critical value = 2.33

Step III: Test Statistics

Step IV: Decision

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