Business Statistics Corresponding Business

Question: Describe about the Business Statistics for Corresponding Business. Answer: Hypotheses Formulation Null Hypothesis (H0): 1 = 2 i.e. there is no significant difference between the reaction times of drivers who are using mobile phones and those who are not using mobile phones Alternative Hypothesis (H1): 1 2 i.e. the reaction times of drivers who are using mobile phones is slower than those who are not using mobile phones Test Result from Excel In the given case, the sample size for both is greater than 30 and also both have been drawn from the same population due to which the relevant test would be two sample z-test for means. The excel output for the z test (Two sample for means) is indicated below. Reaction time on phone Reaction time not on phone Mean 0.775 0.724 Known Variance 0.026 0.038 Observations 100 80 Hypothesized Mean Difference 0 z 1.883 P(Z=z) one-tail 0.030 z Critical one-tail 1.645 P(Z=z) two-tail 0.060 z Critical two-tail 1.960 Analysis and Conclusion It is apparent that the test is one tail and hence the relevant p value to be taken into consideration is 0.03. The significance level given for this test is 5% or 0.05. As the level of significance is greater than the p value, hence rejection of null hypothesis takes place while acceptance of alternate hypothesis happens. Hence, it may be concluded that the reaction time of drivers who use mobile phones is lower than those drivers who do not use mobile phone. 4. Hypotheses Formulation Null Hypothesis (H0): 2014 = 2015 i.e. average shareholders at the end of 2014 and at the end of 2015 are equal. Alternative Hypothesis (H1): 2014 2015 i.e. average shareholders at the end of 2014 was greater than the corresponding shareholdings at the end of 2015. Test Result from Excel Since the test sample are dependent and interrelated due to use of same persons, hence a paired t test for means is the most suitable option and the output of excel in this regard is shown below. Year 2014 ($) Year 2015 ($) Mean 11495.35 10862.54 Variance 37759494.11 47733738.77 Observations 115 115 Pearson Correlation 0.91 Hypothesized Mean Difference 0 df 114 t Stat 2.42 P(T=t) one-tail 0.01 t Critical one-tail 1.66 P(T=t) two-tail 0.02 t Critical two-tail 1.98 Analysis and Conclusion It is apparent that the test is one tail and hence the relevant p value to be taken into consideration is 0.01. The significance level given for this test is 5% or 0.05. As the level of significance is greater than the p value, hence rejection of null hypothesis takes place while acceptance of alternate hypothesis happens. Hence, it may be concluded that indeed there has been a decrease in the shareholdings at the end of 2015 as compared to the corresponding levels at the end of 2014.