Statistics of Business and Finance - Hypothesis Testing and Interpretation
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Added on  2023/06/04
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This study covers hypothesis testing and interpretation in business and finance statistics, including testing mean, associated risk, and returns of General Dynamics and Boeing Company. It also includes the estimation of the CAPM model and residual normality testing.
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STATISTICS OF BUSINESS AND FINANCE STUDENT NAME/ID [Pick the date]
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(1)Return (%) for S&P Price Index, Boeing Company and General Dynamics is given below. 1
Jarque Berra Test to check the normal distribution of the data variables. JBstat=(N 6)(S2+(K−3)2 4) Where, N= Number of observations K = Kurtosis S= Skew value Case 1:Boeing Returns (%) Null hypothesis H0: Variable follows normal distribution. Alternative hypothesis H1: Variable does not follow normal distribution. JB stat = 10.04 The JB stat calculated is lower than critical value and thereby, rejection will not be done for null hypothesis. Hence, Boeing Retunrs follows normaldistribution. Case 2: General DynamicsReturns (%) Null hypothesis H0: Variable follows normal distribution. Alternative hypothesis H1: Variable does not follow normal distribution. JB stat = 33.0 The JB stat calculated is higher than critical value and thereby, rejection will be done for null hypothesis as a result of this rejection, alternative hypotehsis is accepted. Hence,General Dynamicsreturns do not follow normaldistribution. (2)Hypothesis test Claim to test: Mean of General Dynamics Returns is not same as 2.8%. 2
Null hypothesis and alternative hypothesis The population standard deviation = Not given Relevant test stat = t stat Degree of freedom (dof) = 60-1 =59 The two tailed p value = 0.02 Significance level = 5% or 0.05 The key observation is that p value is not higher than significance level which means null hypothesis is rejected and alternative hypothesis is accepted. The claim is right that mean value of General Dynamics Returns is not same as 2.8%. (3)Hypothesis test Claim to test: Associated risk of General Dynamics Returns (GD) and Boeing Company Returns (BA) is not same. Null hypothesis and alternative hypothesis Relevant test stat = F statistic 3
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The two tailed p value = 2* one tailed p value = 0.0086 Significance level = 5% or 0.05 The key observation is that p value is inferior to significance level which means null hypothesis is rejected and alternative hypothesis is accepted. The claim is right that associated risk of General Dynamics Returns (GD) and Boeing Company Returns (BA) is not same. (4)Hypothesis test Claim to test: Return of General Dynamics Returns (GD) and Boeing Company Returns (BA) is not same. Null hypothesis and alternative hypothesis Relevant test stat = t statistic 4
The two tailed p value = 0.8827 Significance level = 5% or 0.05 The key observation is that p value is superior to significance level which means null hypothesis is not rejected and alternative hypothesis is not accepted. The claim is not right that returns of General Dynamics Returns (GD) and Boeing Company Returns (BA) are not same. The stock that would be preferred between the given stocks would be General Dynamics which can be based on the premises that population of the two stock returns tend to have differing risk. However, the returns of the population of the two stocks are not different. This implies that the decision for the preferred stock needs to be made on the basis of risk where the stock with lower risk would be the optimal choice. This is General Dynamics stock. (5) Once the preferred stock is determined, then the excess returns both for the S7P index and the GD stock would be determined considering the treasury rates which serve as the risk free yield.For estimation of the CAPM model the excess returns on the S &P Index serve as the predictor variable while the excess returns on GD stock tends to service as the dependent variable. The CAPM related output is as highlighted below. 5
The equation representing the CAPM model is indicated as follows. GD stock excess returns = 0.111 + (0.642 * Market Excess Returns) (c) R2value is 0.2237 (d) The confidence interval in relation to GD stock bets with 95% confidence lies within the range 0.328 and 0.957. (6) Hypothesis Testing (Confidence Interval Approach) H0(Null Hypothesis): βGD= 1 H1(Alternative Hypothesis): βGD≠1 The hypothesised value for beta is 1 since this value would be indicative of neutral stock. The confidence interval that has been estimated clearly does not contain the value 1. This is indicative of the fact that the null hypothesis rejection would not happen considering the fact that that hypothesised value (i.e.1) is not present in the 95% confidence interval. 6
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PART B: Interpretation (1) In relation to the normal distribution, the relevant inferential test indicates that Boeing stock would have a normal distribution of monthly returns where the GD stock returns would have a non-normal distribution of monthly returns. With regards to evaluation of stock, two parameters hold the key which are underlying risks and return. The risk is captured by the standard deviation of the returns. For the GD stock, the averagemonthlyreturnsarehigherwhencomparedtoBoeingstock.Further,against expectations the risk associated with GD stock is also lower in comparison to the Boeing stock which makes GD stock a superior stock based solely on the sample data. (2) The t student distribution is the appropriate choice to highlight the null hypothesis. Further, the hypothesis test indicates that the average population monthly returns on the GD stock tend to deviate significantly from 2.8%. (3) On the basis of the relevant hypothesis test, it is fair to conclude that deviation does tend to exist between the population risks associated with the monthly returns on the two stocks. (4) On the basis of the relevant hypothesis test, it is fair to conclude that no deviation tends to exist between the population returns associated with the monthly returns on the two stocks. The stock that would be superior is GD since lower risks is associated with GD in comparison with Boeing and also the returns not being different in any significant manner. (5) (b) The stock i.e. GD beta based on CAPM model has come out as 0.642. This implies that whenever the excess market returns tends to undergo any change by 1%, then parallel change in the excess returns on GD stock would be 0.642%. (c) The excess returns on the market has the potential to account for only 22.37% of the total changes that would be apparent in case of excess stock returns (GD stock). This is indicative of the CAPM approach not yielding a model with good fit. (d) The GD stock beta based on the population of monthly returns can be estimated to range between 0.328 and 0.957 with a 95% chance. 8
(6) The confidence interval based hypothesis testing reflects rejection of the claim that GD stock is a neutral stock. (7) For ascertaining the residual normality, the requisite hypothesis testing was carried out and the assumption of the linear regression model in relation to normality of residuals seems satisfied. 9