4. In an attempt to compare the performance of students with more than one personal electronic gadgets and those with no or only one personal electronic gadget, The mean grade in one term and the standard deviation are shown in the table: Students with personal electronic gadgets 0-1 >1 Mean x₁ = 83 x₂ = 79 Standard Deviation Si= 10 S₂ = 14 sample n₁ =12 m₂ = 12 Is there a significant difference in the mean grades of students with one or no personal electronic gadget and those with more than one personal electronic gadgets? @ α = 0.05 and two-tailed test.

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Please use the 5 steps: Step 1: State null & alternate hypothesis Step 2: Select a level of significance Step 3: Identify the test statistic Step 4: Formulate a decision rule Step 5: Take a sample to arrive at a decision (Reject or do not reject null hypothesis) Note: please answer 4-5 only
WEEK 8 EXERCISES: T-test
Test the hypothesis using 5 steps.
1. A ten (10) randomly selected groceries in San Francisco has an average sales
of 41 Junousand dollars every 6 months from various goods with a standard
deviation of 5.2thousand doll ans enough evidence to conclude that the
groceries are not gan average of 42 thousand dollars (μ) from ious
good
y 6 months? Test at 0.05 level of significance. Use one-tailed test.
To
2. A certain manager wishes to find out if the proposed system of operations
increases the gross sales of the products of the compared with ng system.
compare the results, six branches for each system are y selected for
assessment, thet is as follows:
Pro system
x₁ = 42.5,
S₁= 5.7.
Existing system
Average sales in million
X2 = 32.6
Standard deviation:
S₂= 4.8
No. of branches
12- 6
Is the proposed system gnificantly better than the visting system? Test at
a=0.01(1%) and tailed test.
3. Oil wells in large field produce an average of 33.5(µ) bars per day.A
fifteen (15) andomly selected oil wells produce an average of 30 (barrels of
crude of per day with a standard deviation of 3.5 barrels. Is this enough evidence
to conclude that the oil wells are not producing an average of 33.5(µ) barrels of
cade oil per day? Test at
Transcribed Image Text:WEEK 8 EXERCISES: T-test Test the hypothesis using 5 steps. 1. A ten (10) randomly selected groceries in San Francisco has an average sales of 41 Junousand dollars every 6 months from various goods with a standard deviation of 5.2thousand doll ans enough evidence to conclude that the groceries are not gan average of 42 thousand dollars (μ) from ious good y 6 months? Test at 0.05 level of significance. Use one-tailed test. To 2. A certain manager wishes to find out if the proposed system of operations increases the gross sales of the products of the compared with ng system. compare the results, six branches for each system are y selected for assessment, thet is as follows: Pro system x₁ = 42.5, S₁= 5.7. Existing system Average sales in million X2 = 32.6 Standard deviation: S₂= 4.8 No. of branches 12- 6 Is the proposed system gnificantly better than the visting system? Test at a=0.01(1%) and tailed test. 3. Oil wells in large field produce an average of 33.5(µ) bars per day.A fifteen (15) andomly selected oil wells produce an average of 30 (barrels of crude of per day with a standard deviation of 3.5 barrels. Is this enough evidence to conclude that the oil wells are not producing an average of 33.5(µ) barrels of cade oil per day? Test at
a=0.1, level of significance. Use two-tailed test
4. In an attempt to compare the performance of students with more than one
personal electronic gadgets and those with no or only one personal electronic
gadget, The mean grade in one term and the standard deviation are shown in
the table:
Students with personal
electronic gadgets
0-1
>1
Mean
x₁ = 83
x₂ = 79
Standard
Deviation
Mean
Si=10
S₂ = 14
X₁ = 83
X2 = 79
Is there a significant difference in the mean grades of students with one or no personal
electronic gadget and those with more than one personal electronic gadgets? @ a = 0.05
and two-tailed test.
5. Perform Exercise no. 2, assuming one-tailed test, @a= 0.01 and n₁ = 15.
Students with personal
electronic gadgets
0-1
>1
sample
Standard
Deviation
n₁ = 12
m2 =12
Si= 10
S₂= 14
n₁ =15
n₂ = 12
Transcribed Image Text:a=0.1, level of significance. Use two-tailed test 4. In an attempt to compare the performance of students with more than one personal electronic gadgets and those with no or only one personal electronic gadget, The mean grade in one term and the standard deviation are shown in the table: Students with personal electronic gadgets 0-1 >1 Mean x₁ = 83 x₂ = 79 Standard Deviation Mean Si=10 S₂ = 14 X₁ = 83 X2 = 79 Is there a significant difference in the mean grades of students with one or no personal electronic gadget and those with more than one personal electronic gadgets? @ a = 0.05 and two-tailed test. 5. Perform Exercise no. 2, assuming one-tailed test, @a= 0.01 and n₁ = 15. Students with personal electronic gadgets 0-1 >1 sample Standard Deviation n₁ = 12 m2 =12 Si= 10 S₂= 14 n₁ =15 n₂ = 12
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