The accompanying data shows the weekly purchases of printers at a particular electronic store. Using
alpha α equals=0.050
perform a chi-square test to determine if the number of printers sold per week follows a normal probability distribution. Note that
x equals=11.2
and
s equals=4.5
Click the icon to view the weekly purchases of printers.
Use the intervals below to calculate the chi-square test statistic, χ2.
Interval 1: |
z |
≤−1.0 |
|||
---|---|---|---|---|---|
Interval 2:−1.0 |
< |
z |
≤ |
0 |
|
Interval 3: |
0 |
< |
z |
≤ |
1.0 |
Interval 4: |
1.0 |
< |
z |
chi squared χ2 = ?
(Round to two decimal places as needed.)
Determine the p-value.
p-value =??
(Round to three decimal places as needed.)
"blank H0.There "Blank" enough evidence to conclude that the number of printers sold per week at the electronic store does not follow the normal probability distribution.
Let fo and fe be observed and expected frequencies.
Total number of observations, n = 45
Intervals | Area in Class | X = 11.2 + z * 4.5 | fo | fe = Area * 45 | (fo - fe) | (fo - fe)2 | (fo - fe)2/fe |
z |
0.1587 | X |
6 | 7.1415 | -1.1415 | 1.303022 | 0.1824577 |
-1.0 < z |
0.3413 | 6.7 < z |
18 | 15.3585 | 2.6415 | 6.977522 | 0.4543101 |
0 < z |
0.3413 | 11.2 < X |
11 | 15.3585 | -4.3585 | 18.99652 | 1.236873 |
1.0 < z | 0.1587 | 15.7 < X | 10 | 7.1415 | 2.8585 | 8.171022 | 1.14416 |
Area in class are calculated from z tables -
P(z -1.0) = 0.1587
P(-1.0 < z 0) = P(z <0) -
P(z
-1.0) = 0.5 -
0.1587 = 0.3413
P(0 < z 1.0) = P(z <1) -
P(z
0) = 0.8413 - 0.5 =
0.3413
P(z > 1.0) = 0.1587
X =
= 11.2 + z * 4.5
chi-square test statistic X^2 = Sum of (fo - fe)2 /fe = 0.1824577 + 0.4543101 + 1.236873 + 1.14416 = 3.017801
Degree of freedom = k - p - 1
where k is number of intervals
p is number of parameters. Here mean and standard deviation are the parameters. p = 2
Degree of freedom = 4 - 2 - 1= 1
P(X^2 > 3.017801, df = 1) = 0.082355
Thus, p-value is 0.082
The accompanying data shows the weekly purchases of printers at a particular electronic store. Using alpha...
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