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In: Statistics and Probability

What is the 95 percent confidence intervals for the average daily inventory holding cost Pre- and...

What is the 95 percent confidence intervals for the average daily inventory holding cost Pre- and Post- COVID-19 (X_1&〖 X〗_2 )? And what do you conclude by comparing these intervals? Also what is the 99 percent confidence interval for the average daily inventory holding cost Post- COVID-19 (X_2 )? And what do you conclude by comparing the 95 and 99 percent confidence intervals for the average daily inventory holding cost Post- COVID-19 (X_2 )?

Date		1/Nov/2019	2/Nov/2019	3/Nov/2019	4/Nov/2019	5/Nov/2019
Pre-COVID-19	Y1	4614.6	4615.0	4614.6	4614.9	4616.1
Pre-COVID-19	X1	8.4	8.1	9.2	8.4	6.1
Date		1/Apr/2020	2/Apr/2020	3/Apr/2020	4/Apr/2020	5/Apr/2020
Post-COVID-19	Y2	2938.2	2942.9	2937.9	2941.2	2934.4
Post-COVID-19	X2	11.7	8.0	10.2	9.3	11.3

Solutions

Expert Solution

95% Confidence interval for X1

Sample mean of X1 is

Sample standard deviation of X1 is

Degree of freedom = 5-1 = 4

From t-table, for 95% confidence value and degree of freedom =4,

t = 2.776

The 95% Confidence interval is calculated as:

The 95% confidence interval for average daily inventory holding cost Pre- Covid-19 is (6.60, 9.48)

95% Confidence interval for X2

Sample mean of X2 is

Sample standard deviation of X1 is

Degree of freedom = 5-1 = 4

From t-table, for 95% confidence value and degree of freedom =4,

t = 2.776

The 95% Confidence interval is calculated as:

The 95% confidence interval for average daily inventory holding cost Post- Covid-19 is (8.23, 11.97)

Comparing the 95% confidence interval for average daily inventory holding cost for Pre and Post- Covid-19, we see that there is a small overlap in the confidence interval regions of both values. Thus there isn't convincing evidence that average inventory cost for Pre and Post Covid-19 are different.

99 percent confidence interval for tX2

Degree of freedom = 5-1 = 4

From t-table, for 99% confidence value and degree of freedom =4,

t = 4.602

The 99% Confidence interval is calculated as:

The 99% confidence interval for average daily inventory holding cost Post- Covid-19 is (7.00, 14.01)

The 95% confidence interval for X2 is (8.23, 11.97), while the 99% confidence interval is (7.00, 14.01). We can be 95% confidence that the average daily inventory holding cost Post- Covid-19 lies between 8.23 and 11.97 while we can be 99% confidence that the average daily inventory holding cost Post- Covid-19 lies between 7.00 and 14.01.

Comparing both the confidence intervals we conclude that, the 99% confidence interval is significantly wider than the 95% confidence interval.

orchestra answered 1 year ago

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