Data Analysis for Business Decision Making

[Name of the Author]

Table of Contents

Task 11

99% Confidence intervals1

99% CI around Mean Cost1

99% CI around Mean Time2

99% CI around Proportion3

Task 24

Hypothesis testing to test claims4

The Test5

Hypothesis testing to test claims6

The Test7

Task 38

Hypothesis testing to test claims8

The Test9

Reference10

Task 1

99% Confidence intervals

99% CI around Mean Cost

99% Confidence interval around the mean value of the cost is

n = 450Sample mean = =87Sample standard deviation = =7.50

a (at 99% CI) = 0.01/2 = 0.005z score (at a=0.005) = 2.58

When the population standard deviation is unknown 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 estimation

The 99% confidence interval around mean is

Mean ± z score

So the CI around mean cost is

87 2.58 = 87 0.913

Conclusion

The 99% Confidence interval has given us £ 87.91 to £ 86.08 as range for the mean value of the original cost in pound sterling. This interval is estimated for population.

99% CI around Mean Time

99% Confidence interval around the mean length of time in stocks is

n = 450Sample mean = =2.3

Sample standard deviation = =0.38a (at 99% CI) = 0.01/2 = 0.005

z (at 99% CI) = 2.58

When the population standard deviation is unknown 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 estimation

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

The 99% Confidence interval has given us 2.346 to 2.253 weeks as range for the mean length of time in the stocks. This interval is estimated for population.

99% CI around Proportion

99% Confidence interval around the proportion of items which had remained in stock for longer than five weeks is

N = 450P = = =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

The 99% Confidence interval has given us 4.52% to 11.02% range in proportions for the items have remained in stock for more than 5 weeks. This interval is estimated for population.

Task 2

Hypothesis testing to test claims

Method of hypothesis testing is used to find statistically significant evidence of any claim. To find whether there has been a decrease in cost for the distributor's stocked items from the previous period to current or not, z-test of hypothesis is used.

This is a two sample z-test for comparing means. So, the data consist of two sets, namely quarters.

CURRENT QUARTER

PREVIOUS QUARTER

=

450

=

300

Sample Mean = =

87

Sample Mean = =

102

Sample Standard Deviation ==

7.5

Sample Standard Deviation ==

12

Population variance is used to conduct a z test. Since, the population standard deviation is unknown 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

The Test

Null Hypothesis: The difference between the mean cost of items of ...