An entrepreneur was opening a new fitness equipment store and wanted to determin
ID: 3153547 • Letter: A
Question
An entrepreneur was opening a new fitness equipment store and wanted to determine the quantity of each type aerobic equipment she needed to have in inventory. In a previously opened store she opened, historical data showed the following to be monthly sales by machine in terms of percentage of units sold: Treadmill 42% Elliptical 22% Stairmaster 22% Recumbent 14% She sold 200 total units in the first month of business with the following distribution: Treadmill 91 Elliptical 35 Stairmaster 47 Recumbent 27 THESE ARE THE OBSERVED VALUES If her expected sales are to match her previous store, did her observed values equal her expected values at a 5% level of significance? Use and show the 5-step process along with any supporting information. Expected Values Treadmill 200 time sign.42 = 84 Eliptical 200 time sign.22 = 44 Stairmaster 200 time sign.22 = 44 Recumbent Bike 200 time sign. 14 = 28 Step 1: Ho: Ha: Step 2: alpha = Step 3: Test Statistic: Step 4: Decision Rule Step 5: Calculation and Decision x^2 = sigma ((integral_o - integral_e)^2/integral_e) = Reject or Do Not Reject the HoExplanation / Answer
Goodness of Fit Test
observed
expected
O - E
(O - E)² / E
91
84.000
7.000
0.583
35
44.000
-9.000
1.841
47
44.000
3.000
0.205
27
28.000
-1.000
0.036
200
200.000
0.000
2.665
2.665
chi-square
3
df
Ho: The observed values equal the previous expected values.
Ho: The observed values did not equal the previous expected values.
Test statistic =Chi square test
Decision Rule: if calculated chi square > 7.815, critical value of chi square at 5% level, Reject Ho.
Calculated chi square =2.665
Calculated chisquare =2.665 < 7.815, do not reject Ho.
We conclude that the observed values equal the previous expected values.
Goodness of Fit Test
observed
expected
O - E
(O - E)² / E
91
84.000
7.000
0.583
35
44.000
-9.000
1.841
47
44.000
3.000
0.205
27
28.000
-1.000
0.036
200
200.000
0.000
2.665
2.665
chi-square
3
df