Business Statistics Module six Assignment

Business Statistics Module six Assignment
Student’s Name
Institution Affiliation

Question One
a. Influence of a large number of package type on the value of Chi-square
statistics
According to Stine& Foster (2014), large sample increases the Chi- Square statistics. Therefore,
a large number of package types will result in a large value of Chi- square statistics.
b.
When the independency of null hypothesis holds, chi-squared statistics are not directly compared
between two tables of different dimensions, as they are comparable only with contingency table,
for example, 2x2 contingency table, due to fact that dissimilar dimensional tables produce
different results. This rule is applied to avoid a rejection of the null hypothesis when it’s
statistically significant.
c. Explaining whether Cramer’s V be used instead of p-values to standardize the
results.
For standardization of the results, Cramer’s V will not be employed instead of p-value as it’s
only indicate the effect size of the Chi-square statistics as opposed to p-value which shows
whether Chi-square statistics is statistically significant or not.
Advantages of p-values over Cramer’s’ V
P-values help in decision making about the null hypothesis. The rejection or the adoption of
null hypothesis depends on the p-value which p-values p-value which is subjected to a specified
degree of significance say 5%. When the computed p-value is below this level of
significance null hypothesis is reject and above this level null hypothesis is adopted(Ruppert,
2014). The Cramer’s V on the other hand will be used to determine the effect size of the

statistics, which helps in determination of the accuracy of test statistics. The Cramer V
below 0.20 indicates small effect, above 0.20 shows medium effect and, 0.70 and above shows
large effect (Stine& Foster (2014).
Disadvantages of p-values
When the p-values is higher than the significance level, the results of the Chi-square
statistics is not efficient and the Cramer’s V will show small effects which indicate
decreases importance of Chi-square.
d. Average value of 69 chi-squared statistics, given that of the 650 products, 69 comes
in 5 types of packaging.
The average will be given by
Average= Number of products
Number of types of packaging = 69
5 =13.80
Therefore, the average value of 69 Chi-Square Statistics is 13.80
Question Two
a.
The probability of a single p-value been above 0.05 is 0.95, therefore the probability for the 50 p-
values been less than 0.05 will be given
prob( p<0.05)=1−0.95n , where nis he number of products
1−0.9550=0.9231
The number of p-values which are less than 0.05 will be given by
np=50∗0.9231=46.15 ≈ 46 pvalues