Original Cost of the Product - Coursework Example

99% Confidence Interval for the proportion of items that had remained in stocks for longer than 5 weeks

For 99% confidence, z = 2.576.
The true percentage of items that had remained in stocks for longer than 5 weeks is between 4.53% and 11.03% with 99% confidence.

Task 2
Research Question 1
The research question examined is “Has there been a decrease in cost for the distributor’s stocked items from the previous period to the current?” The null and alternate hypotheses tested are

(1-Current Period, 2-Previous Period)
The selected level of significance, α is 5%.
The selected test is Two Large Independent Samples z-Test, as both sample sizes are large (n1 = 450 > 30 and n2 = 300 > 30).
At the level of significance of 5%, the critical value for the one-tailed (left-tailed) test is -1.645. Therefore, the decision rule will be
Reject H0, if z < -1.645. Otherwise, do not reject H0.


The value of the test statistic, z = -19.28 is less than the critical value of -1.645, thus rejecting the null hypothesis H0. Thus, there is enough evidence to conclude that there has been decreasing in cost for the distributor’s stocked items from the previous period to the current.

Research Question 2
The research question examined is “Is there a difference in the proportion of slow-moving stock?” The null and alternate hypotheses tested are

(1-Current Period, 2-Previous Period)
The selected level of significance, α is 5%.
The selected test is the Two Independent Proportions z-Test.
At the level of significance of 5%, the critical values for the two-tailed test are -1.960 and +1.960. Therefore, the decision rule will be
Reject H0, if z < -1.960 or z > 1.960. Otherwise, do not reject H0.


The value of the test statistic, z = -2.750 is less than the left-tail critical value of -1.960, thus rejecting the null hypothesis H0. Thus, there is enough evidence to conclude that there is a difference in the proportion of slow-moving stock.
In conclusion, there has been decreasing in cost for the distributor’s stocked items from the previous period to the current and there is a difference in the proportion of slow-moving stock from the previous period to the current.

Task 3
The null and alternate hypotheses tested are


The selected level of significance, α is 5%.
The selected test is One Sample z-Test, as the population standard deviation is known.
At the level of significance of 5%, the critical values for the two-tailed test are -1.960 and +1.960. Therefore, the decision rule will be
Reject H0, if z < -1.960 or z > 1.960. Otherwise, do not reject H0.

In conclusion, the claim that the average content is 490 units per box is incorrect. There is strong evidence that the content size is less than 490 units per box. Read More