Data Analysis for Business Decision Making

[Name of the Author]

Table of Contents

Task 11

Confidence intervals1

For Cost1

For Time2

For Proportion3

Task 24

Hypothesis testing for difference between means4

Z-test5

Hypothesis testing for difference between proportions6

Z-test7

Task 38

Testing of Supplier's claims (When n is small)8

t-test9

Reference10

Task 1

Confidence intervals

For Cost

Confidence interval around the mean value of the cost will be calculated using the following data

n = 450

=87

=7.50

a (at 99% CI) = 0.01/2 = 0.005

z (at 99% CI) = 2.58

The population standard deviation in this case is unknown (which is mandatory in CI around mean for normal distribution). Still, if n>30, the sample standard deviation is assumed to be an unbiased estimator of population standard deviation after application of some adjustment.

Adjusting the sample standard deviation for normalization

The 99% confidence interval around mean is

Mean ± z score

So the CI around mean cost is

87 2.58 = 87 0.913

Conclusion

Through Confidence interval, we can be 99% confident that the population mean lies in the range of 87.91 to 86.08.

For Time

Confidence interval around the mean length of time in stocks will be calculated using the following data

n = 450

Sample mean = =2.3

Sample standard deviation = =0.38

a (at 99% CI) = 0.01/2 = 0.005

z (at 99% CI) = 2.58

The population standard deviation in this case is unknown ( which is mandatory in CI around mean for normal distribution). Still, if n>30, the sample standard deviation is assumed to be an unbiased estimator of population standard deviation after application of some adjustment.

Adjusting the sample standard deviation for normalization

The 99% confidence interval around mean is

Mean ± z score

So the CI around mean length of time in stocks is

2.3 2.58 = 2.3 0.046

Conclusion

Through Confidence interval, we can be 99% confident that the mean length of time in the stocks consisting of whole population lies in the range of 2.346 weeks to 2.2538 weeks

For Proportion

Confidence interval around the proportion of items which had remained in stock for longer than five weeks is calculated using the following data.

N = 450

P = = =0.077

The 99% confidence interval around proportion is

Proportion ± z score

So the 99% CI around proportion is

0.077 2.58 = 0.077 0.0325 = 0.0452 to 0.1102

Conclusion

Through Confidence interval, we can be 99% confident that approximately 11.02% to 4.52% of the items have remained in stock for more than 5 weeks

Task 2

Hypothesis testing for difference between means

A hypothesis test, namely z - test, will give statistically significant evidence of whether there has been a decrease in cost for the distributor's stocked items from the previous period to current or not.

For this test, the following data will be used

There are two data sets one consists of the current quarter and the other consists of the previous quarter

CURRENT QUARTER

PREVIOUS QUARTER

=

450

=

300

Sample Mean = =

87

Sample Mean = =

102

Sample Standard Deviation ==

7.5

Sample Standard Deviation ==

12

The population standard deviation in this case is unknown (which is mandatory for conducting z-test). Still, if n>30, the sample standard deviation is assumed to be an unbiased estimator of population standard deviation after application of some adjustment.

Adjusting the sample standard deviation for normalization

For current quarter

For previous quarter

Z-test

Null Hypothesis: ...