Data of variable-A is collected as shown to the right. Is the mean of Variable-A less than 80? State null hypothesis and choose level of significance, a = 0.05. (Use Excel ttest function, provide clear logic and reasoning.) Variable-A Variable-B 78.8 81.9 76.9 78.0 67.8 69.7 68.9 74.7 70.5 70.0 80.0 68.2 63.0 88.7 78.7 86.7 85.4 69.5 87.0 75.1 82.4 71.8 78.2 58.1 76.9 74.8 60.2 93.2 82.6 84.6 67.2 66.5 71.7 77.2 68.9 74.0 69.3 77.7 89.1 78.6 76.3 68.3 74.0 89.0 69.4 82.1 76.3 78.0 66.2 80.3 73.9 82.4 79.1 83.1 80.4 66.4 66.2 67.6 80.9 75.3
Data of variable-A is collected as shown to the right.
- Is the mean of Variable-A less than 80? State null hypothesis and choose level of significance, a = 0.05. (Use Excel ttest
function , provide clear logic and reasoning.)
|
Variable-A |
Variable-B |
|
78.8 |
81.9 |
|
76.9 |
78.0 |
|
67.8 |
69.7 |
|
68.9 |
74.7 |
|
70.5 |
70.0 |
|
80.0 |
68.2 |
|
63.0 |
88.7 |
|
78.7 |
86.7 |
|
85.4 |
69.5 |
|
87.0 |
75.1 |
|
82.4 |
71.8 |
|
78.2 |
58.1 |
|
76.9 |
74.8 |
|
60.2 |
93.2 |
|
82.6 |
84.6 |
|
67.2 |
66.5 |
|
71.7 |
77.2 |
|
68.9 |
74.0 |
|
69.3 |
77.7 |
|
89.1 |
78.6 |
|
76.3 |
68.3 |
|
74.0 |
89.0 |
|
69.4 |
82.1 |
|
76.3 |
78.0 |
|
66.2 |
80.3 |
|
73.9 |
82.4 |
|
79.1 |
83.1 |
|
80.4 |
66.4 |
|
66.2 |
67.6 |
|
80.9 |
75.3 |
Data of variable-A is entered in a spreadsheet.
Therefore,
sample mean = = 74.87
This is calculated using the '=AVERAGE(cell range)' function.
sample standard deviation = s = 7.24
This is calculated using the '=STDEV.S(cell range)' function.
Let the population mean be
The data size (n) is given to be 30.
The null hypothesis to be tested for this problem is -
while the alternative hypothesis is-
level of significance a is given to be 0.05.
From the alternative hypothesis it can be said that the test being performed is the left-tailed test.
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