Research Methods for Business - Assignment Example

Research Methods for Business College: Question Is there any evidence of an association between occupational status and the number of visits to the Gymnasium during the past four weeks? Carry out an appropriate hypothesis test In this regards, we will use correlation to test the relationship between the two groups. According to the table below (Appendix 1), the P value is 0.05 and it is less than 0.05.This implies that we fail to reject the null hypothesis that there is an association between the two groups. The correlation is negative and weak (-0.177) we then conclude that the evidence that an association between occupational status and the number of visits to the Gymnasium do exist. Correlations Occupation Visits Occupation Pearson Correlation 1 -.177* Sig. (2-tailed) .015 N 188 188 Visits Pearson Correlation -.177* 1 Sig. (2-tailed) .015 N 188 188 *. Correlation is significant at the 0.05 level (2-tailed). Question 2) Is there any evidence that the average customer satisfaction score is age-dependent? Carry out an appropriate hypothesis test. In this case, we will use regression analysis to see if the average customer satisfaction is dependent on the age. Basing on the analysis as shown below (Appendix 2), it is clearly evident that the customer satisfaction is not dependent on the age. This is shown by the p value (0.813) which is greater than 0.05.Hence in this case we reject the null hypothesis. Therefore, we conclude that the average customer satisfaction is not dependent on the age. Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .017a .000 -.005 1.066 a. Predictors: (Constant), Age Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 3.686 .175 21.035 .000 Age .021 .090 .017 .237 .813 a. Dependent Variable: satsfaction level Question 3) The Gymnasium management have calculated that a monthly membership fee of at least £75 will be required to cover the investment and running costs of the upgraded Gymnasium. Test the null hypothesis that the mean willingness-to-pay for membership of the upgraded Gymnasium is at least £75, against the one-sided alternative hypothesis that the mean willingness to pay is less than £75. The appropriate test for this question is one sample t test. According to the results as shown below (Appendix 3), the calculated t value is greater than the critical value. Therefore, we reject the null hypothesis and conclude that the mean willingness to pay is less than £75.The P value is less than 0.05 alpha. This means that the calculated t value is statistically significant. One-Sample Test Test Value = 75 t df Sig. (2-tailed) Mean Difference 95% Confidence Interval of the Difference Lower Upper Monetary -4.440 187 .000 -5.947 -8.59 -3.30 Question 4) Test whether there is any evidence of a difference between the willingness-to-pay for membership of the upgraded Gymnasium of male and female customers. Independent sample t test is the appropriate test to test whether there is any evidence of a difference in the willingness-to- pay for membership between male and female customers. According to the results below (Appendix 4), it is clearly evident that there is a difference in the willingness of the paying of the membership between men and women. The p value is less than 0.05; this means that the calculated t value (4.824) is statistically significant. The calculated t value is greater than the critical value. This means that we reject the null hypothesis Therefore we conclude that there is enough evidence that there is a difference in the willingness-to- pay for membership between male and female customers. Group Statistics Genda N Mean Std. Deviation Std. Error Mean Monetary 0 129 64.50 15.220 1.340 1 59 79.02 20.705 2.696 Independent Samples Test Levenes Test for Equality of Variances t-test for Equality of Means F Sig. t df Sig. (2-tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference Lower Upper Monetary Equal variances assumed 19.826 .000 -5.397 186 .000 -14.521 2.691 -19.829 -9.213 Equal variances not assumed -4.824 87.782 .000 -14.521 3.010 -20.503 -8.538 Question 5) Estimate a two-variable linear regression to describe the relationship between household weekly net income and willingness-to-pay for membership of the upgraded Gymnasium. According to this regression, what is the estimated willingness-to-pay of a customer with a household weekly net income of £300? According to the analysis results as shown below (Appendix 5), the model is statistically significant since the p value is less than 0.05. The R squared is 0.368 The model equation is Willingness-to-pay of a customer = (0.36) weekly net income +58.72 Using the above equation, we can estimate willingness-to-pay of a customer as 0.36x300+58.72 =166.72. Therefore the estimate is 166.72. Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .368a .135 .131 17.122 a. Predictors: (Constant), Weekly Income Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 58.721 2.287 25.676 .000 Weekly Income .036 .007 .368 5.393 .000 a. Dependent Variable: Monetary Question 6) Estimate a multiple regression in which willingness-to-pay for membership of the upgraded Gymnasium is explained by the following characteristics: gender (male/female), occupational status, and household weekly net income. Basing on the analysis results shown below (Appendix 6), the model equation is as follows: willingness-to-pay for membership=13.506( gender) – 1.796 (occupational status) + 0.026(weekly net income)+ 61.862 Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .515a .265 .253 15.866 a. Predictors: (Constant), Weekly Income, Gender, Occupation ANOVAa Model Sum of Squares df Mean Square F Sig. 1 Regression 16737.045 3 5579.015 22.164 .000b Residual 46316.423 184 251.720 Total 63053.468 187 a. Dependent Variable: Monetary b. Predictors: (Constant), Weekly Income, Gender, Occupation Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 61.862 4.862 12.722 .000 Gender 13.506 2.501 .342 5.400 .000 Occupation -1.796 1.132 -.132 -1.587 .114 Weekly Income .026 .008 .261 3.135 .002 a. Dependent Variable: Monetary i) Comment on the significance of each of these characteristics as determinants of willingness-to-pay. According to the results output, it is observed that gender and weekly income have a positive influence on the willingness-to-pay for membership. Gender has a coefficient of 13.506 while weekly income has 0.26.In this case; gender has a bigger influence as compared to the weekly income. On the other hand, the occupation has a negative influence on the willingness-to-pay. The coefficient is -1.796.Both gender and weekly income coefficients are statistically significant because the p value is less than 0.05.On the other hand, the coefficient of occupation is not statistically significant, this is because its p value is greater than 0.05.In this case it does not suite the model and is required to be eliminated. ii) Comment briefly on the comparison between the multiple regression estimated in Q6 and the two-variable linear regression estimated in Q5. For the multiple regression in Q6 has the weekly income coefficient which is lower than that in the linear regression in question 5.The probable reason for this could be because of co-linearity between the variables that resulted to the value being lowered. iii) What is the estimated willingness-to-pay of a male self-employed customer with a household weekly net income of £500? Willingness-to-pay for membership=13.506( gender) – 1.796 (occupational status) + 0.026(weekly net income)+ 61.862 As seen above that the occupation does not fit in the equation, we must remove it from the model and the final model equation is Willingness-to-pay for membership=13.506(gender) + 0.026(weekly net income)+ 61.862 Therefore the estimate of willing to pay by a male is Willingness-to-pay for membership by a self employed male =13.506+0.026X500+61.862 =88.368 iv) What is the estimated willingness-to-pay of a female employed customer with a household weekly net income of £400? The following equation is used Willingness-to-pay for membership=13.506(gender) + 0.026(weekly net income) + 61.862 Willingness-to-pay for membership=13.506+400X0.026+61.862 =85.768 Reference Dey, I. (1993).Quantitative Data Analysis: A User-friendly Guide for Social Scientists. London, New York: Routledge. Appendix 1 CORRELATIONS /VARIABLES=q3 q5 /PRINT=TWOTAIL NOSIG /MISSING=PAIRWISE. Correlation Correlations Occupation Visits Occupation Pearson Correlation 1 -.177* Sig. (2-tailed) .015 N 188 188 Visits Pearson Correlation -.177* 1 Sig. (2-tailed) .015 N 188 188 *. Correlation is significant at the 0.05 level (2-tailed). Appendix 2 REGRESSION /MISSING LISTWISE /STATISTICS COEFF OUTS R ANOVA /CRITERIA=PIN(.05) POUT(.10) /NOORIGIN /DEPENDENT q7 /METHOD=ENTER q2. Variables Entered/Removeda Model Variables Entered Variables Removed Method 1 Ageb . Enter a. Dependent Variable: satsfaction level b. All requested variables entered. Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .017a .000 -.005 1.066 a. Predictors: (Constant), Age ANOVAa Model Sum of Squares df Mean Square F Sig. 1 Regression .064 1 .064 .056 .813b Residual 211.553 186 1.137 Total 211.617 187 a. Dependent Variable: satsfaction level b. Predictors: (Constant), Age Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 3.686 .175 21.035 .000 Age .021 .090 .017 .237 .813 a. Dependent Variable: satsfaction level Appendix 3 T-TEST /TESTVAL=75 /MISSING=ANALYSIS /VARIABLES=q6 /CRITERIA=CI(.95). One-Sample Statistics N Mean Std. Deviation Std. Error Mean Monetary 188 69.05 18.363 1.339 One-Sample Test Test Value = 75 t df Sig. (2-tailed) Mean Difference 95% Confidence Interval of the Difference Lower Upper Monetary -4.440 187 .000 -5.947 -8.59 -3.30 Appendix 4 T-TEST GROUPS=q1(0 1) /MISSING=ANALYSIS /VARIABLES=q6 /CRITERIA=CI(.95). Group Statistics Genda N Mean Std. Deviation Std. Error Mean Monetary 0 129 64.50 15.220 1.340 1 59 79.02 20.705 2.696 Independent Samples Test Levenes Test for Equality of Variances t-test for Equality of Means F Sig. t df Sig. (2-tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference Lower Upper Monetary Equal variances assumed 19.826 .000 -5.397 186 .000 -14.521 2.691 -19.829 -9.213 Equal variances not assumed -4.824 87.782 .000 -14.521 3.010 -20.503 -8.538 Appendix 5 REGRESSION /MISSING LISTWISE /STATISTICS COEFF OUTS R ANOVA /CRITERIA=PIN(.05) POUT(.10) /NOORIGIN /DEPENDENT q6 /METHOD=ENTER q4. Variables Entered/Removeda Model Variables Entered Variables Removed Method 1 Weekly Incomeb . Enter a. Dependent Variable: Monetary b. All requested variables entered. Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .368a .135 .131 17.122 a. Predictors: (Constant), Weekly Income ANOVAa Model Sum of Squares df Mean Square F Sig. 1 Regression 8525.723 1 8525.723 29.082 .000b Residual 54527.745 186 293.160 Total 63053.468 187 a. Dependent Variable: Monetary b. Predictors: (Constant), Weekly Income Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 58.721 2.287 25.676 .000 Weekly Income .036 .007 .368 5.393 .000 a. Dependent Variable: Monetary Appendix 6 REGRESSION /MISSING LISTWISE /STATISTICS COEFF OUTS R ANOVA /CRITERIA=PIN(.05) POUT(.10) /NOORIGIN /DEPENDENT q6 /METHOD=ENTER q1 q3 q4. Variables Entered/Removeda Model Variables Entered Variables Removed Method 1 Weekly Income, Genda, Occupationb . Enter a. Dependent Variable: Monetary b. All requested variables entered. Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .515a .265 .253 15.866 a. Predictors: (Constant), Weekly Income, Genda, Occupation ANOVAa Model Sum of Squares df Mean Square F Sig. 1 Regression 16737.045 3 5579.015 22.164 .000b Residual 46316.423 184 251.720 Total 63053.468 187 a. Dependent Variable: Monetary b. Predictors: (Constant), Weekly Income, Genda, Occupation Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 61.862 4.862 12.722 .000 Genda 13.506 2.501 .342 5.400 .000 Occupation -1.796 1.132 -.132 -1.587 .114 Weekly Income .026 .008 .261 3.135 .002 a. Dependent Variable: Monetary Read More