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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
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
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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