Statistical Inference for Business Decisions

Statistical Inference for Business Decisions

Practical Application Scenario 1

Null Hypothesis: There is no difference in mean ammunition price of Gander's and Cabela's

Alternate Hypothesis: The mean ammunition price of Gander is lower than Cabela's

Sampling Method

Stratified random sampling is a method of sampling which gives more focus to the attributes of individual members of the population. It is more precise and accurate than simple random sampling. In stratified random sample population is subdivided into smaller groups of similar attributes. Then, a simple random sample of each stratum is taken according to the proportion of stratum's size compared to the population. Since hunting ammunition are not uniform in nature, and since they come in different bore sizes and attributes, the method of stratified random sampling is the most appropriate technique to gather data for this hypothesis.Appropriate test

The t - test with equal variances should be use to test the null and alternate hypothesis in this scenario.

Practical Application Scenario 2

Descriptive Statistics of the Sample:

Current

 

New

 

Mean

270.275

Mean

267.5

Standard Error

1.383968421

Standard Error

1.564837994

Median

270

Median

265

Mode

272

Mode

263

Standard Deviation

8.752984839

Standard Deviation

9.896904463

Sample Variance

76.61474359

Sample Variance

97.94871795

Kurtosis

-0.762587222

Kurtosis

-0.514586551

Skewness

0.306169371

Skewness

0.239810448

Range

34

Range

39

Minimum

255

Minimum

250

Maximum

289

Maximum

289

Sum

10811

Sum

10700

Count

40

Count

40

Z-test:

Null Hypothesis: The difference between mean driving distance of Unidun type (µ1) and SF type (µ2) is zero.

Alternate Hypothesis: The mean driving distance of Unidun type (µ1) is greater than SF type (µ2).

Mathematically,

H?: µ1 - µ2 = 0

Ha: µ1 - µ2 > 0

Level of Significance:

a=0.05

Test Statistics:

z-Test: Two Sample for Means

a=0.05

 

Current

New

Mean

270.275

267.5

Known Variance

76.614

97.948

Observations

40

40

Hypothesized Mean Difference

0

z

1.32836715

P(Z<=z) one-tail

0.09202842

z Critical one-tail

1.64485363

P(Z<=z) two-tail

0.18405684

z Critical two-tail

1.95996398

 

Decision:

Since the Z statistics (z=1.32836715) lie within the z critical value (z critical = 1.64485363), the null hypothesis that “The difference between mean driving distance of Unidun type (µ1) and SF type (µ2) is zero” is accepted. The p - value is 0.09202842

Explanation to the Vice President

The new balls are more able in straight flight and there driving distance, when compared to the older ones, is same. A sample was drawn and a statistical hypothesis ...