SPC & Statistics We ed the data on a statistical package Minitab, and we analysed the data as follows. A) Descriptive statistics
Table 1
Descriptive statistics
Product weight
Count
20
Mean
9. 835
sample variance
0. 163
sample standard deviation
0. 404
minimum
8. 9
maximum
10. 4
Range
1. 5
skewness
-0. 421
kurtosis
0. 077
coefficient of variation (CV)
4. 11%
1st quartile
9. 600
Median
9. 850
3rd quartile
10. 125
interquartile range
0. 525
Mode
9. 900
A population sample N = 20 with a population mean μ = 9. 8. The SD = 0. 4 and a Range of 1. 5.
B) Histogram and normal curve
The graph indicates a Platykurtic distribution as Kurtosis = 0. 07 indicating that most values are around the mean and also indicates an asymmetrical distribution with a negative skew. = -0. 42.
The graph shows a linear correlation between the product weight and the percentage of occurring at a mean 9. 8 and SD = 0. 40. Hence, the normality test indicates that the distribution data sample is normal.
C) At +/- 1. 96 σ
= 95% from the graph above of normality test real score = 10. 5
and +/-3σ
= At 99% from the graph the real score = 10. 8
D). Confidence Intervals 95%
CI = ((9. 8-1. 96*0. 09), (9. 8+1. 96*0. 09))
At 95% = [9. 6, 10] an indication that the mean lies between the product weight and the sample rate can lie between 9. 6 to 10
E)
One-Sample T
Test of μ = 10 vs ≠ 10
N Mean StDev SE Mean 95% CI T P
20 9. 8350 0. 0904 0. 0202 (9. 7927, 9. 8773) -8. 16 0. 000
P-value < . 05 Thus, we reject null hypothesis. Type I error occurs by indicating that the two product weights mean are not equal. Hence, the product weight is almost equal, and the mean lies in between 95% CI.