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Thus, there is enough evidence to conclude that there has been decrease in cost for the distributor’s stocked items from the previous period to the current.
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Task 99% Confidence Interval for the mean value (original cost) Using the normal distribution, as sample size is large (n = 450 > 30). For 99% confidence, z = 2.576.

The true mean value of the original cost of the item is between £86.09 and £87.91 with 99% confidence.
99% Confidence Interval for the mean length of time in stock (in weeks)
Using the normal distribution, as sample size is large (n = 450 > 30).
For 99% confidence, z = 2.576.

The true mean value of the length of time the item has remained in the warehouse is between 2.254 weeks and 2.346 weeks with 99% confidence.
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 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 one-tailed (left-tailed) test is -1.645. Therefore, decision rule will be
Reject H0, if z < -1.645. Otherwise, do not reject H0.
The standard error of the difference is

The test statistic is

The value of test statistic, z = -19.28 is less than the critical value of -1.645, thus reject null hypothesis H0. Thus, there is enough evidence to conclude that there has been decrease 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 Two Independent Proportions z-Test.
At the level of significance of 5%, the critical values for two-tailed test are -1.960 and +1.960. Therefore, decision rule will be
Reject H0, if z < -1.960 or z > 1.960. Otherwise, do not reject H0.
The two proportions are

So,

The standard error of the difference is

The test statistic is

The value of test statistic, z = -2.750 is less than the left-tail critical value of -1.960, thus reject 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 decrease 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
(Claim)
The selected level of significance, α is 5%.
The selected test is One Sample z-Test, as population standard deviation is known.
At the level of significance of 5%, the critical values for two-tailed test are -1.960 and +1.960. Therefore, decision rule will be
Reject H0, if z < -1.960 or z > 1.960. Otherwise, do not reject H0.
The test statistic is

The value of test statistic, z = -10.42 is less than the critical value of -1.960, thus reject null hypothesis H0. Thus, there is enough evidence to conclude that the mean content size is different from 490 units per box.
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
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