(Tiểu luận) business statistics

Trường Đại học Kinh tế Quốc dân o0o BUSINESS STATISTICS Group Name : Nguyễn Trần Nhật Anh Nguyễn Thị Mai Anh Trương Minh Ánh Nguyễn Công Bách Lê Ngọc Hải Vũ Kiều Trang Vũ Thu Trang MSV: 11219023 MSV: 11219021 MSV: 11219032 MSV: 11219033 MSV: 11219055 MSV: 11219141 MSV: 11219143 Khóa: 63 Class : E-BBA 13.3 Hà Nội – 06/2023 I CHAP 12 Problem Independence of responses seemed to be unaffected by the party affiliation but the answers to three questions had mixed reviews Through the table we can see that the lower the mean, the higher the negative Because the number of people choosing yes counts as 1, the smaller the mean, the more negative it is The first question regarding the legislative pay cut for each day the state budget is delayed received the least positive responses with only mean=129 compared to the average responses to the restriction for campaigners the corridor is mean=130 The highest response received when respondents were asked about a fixed-year requirement such as a term limit for serving legislators was mean =141 Problem In order to test for independence of the responses to the three questions (Yes, No) asked to respondents irrespective of party affiliation, the tentative assumption regarding the null hypothesis is that two categorical variables-responses and party affiliation were independent If sample data leads to rejection of null hypothesis, it could be concluded that the responses and the party affiliation were not independent The hypothesis when represented in symbols are as follows: : The responses were independent of party affiliation : The responses were not independent of party affiliation Using excel, the given data is arranged in contingency table is shown below: This is a preview Do you want full access? Go Premium and unlock all 19 pages Access to all documents Get Unlimited Downloads Improve your grades From the above screenshot, the Uploadstatisticsis10.19 The P-value is 0.0061 Share your documents to unlock It is given that the level of the significance is 0.05 Here, it can be observed that the P - value is less than the given level of the significance So, the null hypothesis should be rejected Therefore, it can be concluded that there is sufficient evidence to support that responses were not independent of party affiliation Problem Free Trial Get 30 days of free Premium In order to test for independence of the responses to the three questions (Yes, No) asked to respondents irrespective of party affiliation, the tentative assumption regarding the null hypothesis is that two categorical variables-responses and party affiliation were independent If sample data leads to rejection of null hypothesis, it could be concluded that the responses and the party affiliation were not independent Already Premium? Log in The hypothesis when represented in symbols are as follows: : The responses were independent of party affiliation : The responses were not independent of party affiliation Using excel, the given data is arranged in contingency table is shown below: From the above screenshot, the statistics is 3.72 The P- value is 0.1557 It is given that the level of the significance is 0.05 Here, it can be observed that the P-value is greater than the given level of the significance So, the null hypothesis fails to be rejected Therefore, it can be concluded that there is insufficient evidence to support that responses were independent of party affiliation Problem In order to test for independence of the responses to the three questions (Yes, No) asked to respondents irrespective of party affiliation, the tentative assumption regarding the null hypothesis is that two categorical variables-responses and party affiliation were independent If sample data leads to rejection of null hypothesis, it could be concluded that the responses and the party affiliation were not independent The hypothesis when represented in symbols are as follows: : The responses were independent of party affiliation : The responses were not independent of party affiliation Using excel, the given data is arranged in contingency table is shown below: From the above screenshot, the statistics is 5.11 The P- value is 0.0776 It is given that the level of the significance is 0.05 Here, it can be observed that the P- value is greater than the given level of the significance So, the null hypothesis fails to be rejected Therefore, it can be concluded that there is insufficient evidence to support that responses were independent of party affiliation Problem As per the analysis there appears to be broad support for change across all political lines with respect to more restrictions on lobbyists Because there appears to be no relation between the responses and the political parties that the respondents belong to II CHAP 13 Problem *Calculation: The data represents the survey results obtained to study the relationship between the years of experience and salary for individuals employed in inside and outside sales positions The respondents were asked to specify one of the levels of years of experience: low, medium and high Descriptive statistics for the salary of individuals who employed inside sales position are shown below: Output using EXCEL is given as follows: Thus, the descriptive statistics for the years of experience and salary for individuals employed in inside sales positions is obtained Output using EXCEL is given as follows: This is a preview Do you want full access? Go Premium and unlock all 19 pages Access to all documents Get Unlimited Downloads Improve your grades Upload Thus, the descriptive statistics for theyearsofexperience and salary for individuals employed in outside sales positions is obtained Output using EXCEL is given asSharefollows:your documents to unlock Free Trial Get 30 days of free Premium Already Premium? Log in Thus, the descriptive statistics for the years of experience and salary for individuals employed in all sales positions is obtained The mean annual salary for sales persons regardless of years of experience and type of position is $64,925.48 and the standard deviation is $10,838.67 The mean salary for 'Inside' sales persons is $56,020.52 and the standard deviation is $3589.83 The mean salary for “Outside” salesperson is S73,830.43 and the standard deviation is $7,922.96 The mean salary and standard deviation for “Outside” salespersons is higher compared with the mean salary for “Inside” sales persons The mean salary for sales persons who have “Low” years of experience is $59,819.63 and the standard deviation is $6,005.06 The mean salary for sales persons who have “Medium” years of experience is $68,618.13 and the standard deviation is $13,621.38 The mean salary for sales persons who have “High” years of experience is $66,338.68 and the standard deviation is $9,699.51 The mean salary and standard deviation for sales persons who have “Medium” years of experience is higher compared with the mean salary for sales persons who have “Low” years of experience and “High” years of experience Question 2: *Calculation: Here, 120 observations is considered as the sample and the population standard deviation is not known Hence, t-test can be used for finding confidence intervals for testing population means The level of significance is 0.05 Hence, The 95% confidence interval for the mean annual salary for all sales persons regardless of years of experience and type of position is, < µ < From part (a), substitute, , , in the above formula Independent variable X3 explains 74.16% of the variation in the dependent variable or this linear regression model is appropriate for the amount of X3 data at 74.16% - The influence of the independent variable Top 10 (β4) on the dependent variable Y We see R Square = 0.8059 => Independent variable X4 explains 80.59% of the variation in the dependent variable or this linear regression model is appropriate for the amount of X4 data at 80.59% Conclusion: We see that the independent variable X4 has the highest R Square (0.8059), so we can conclude that Top 10 is the best single tool for predicting winnings Problem This is a preview Do you want full access? Go Premium and unlock all 19 pages Access to all documents Get Unlimited Downloads Improve your grades We obtain the regression equation: Upload-12938.92×X + 13544.81×X + Winnings (Y) = 3140367.087 71629.39×X3 + 117070.57×X4 Share your documents to unlock From this regression equation, we can draw some conclusions: - For each unit increase in X1 (Poles), Y (Winnings) will decrease by $12938.92, and vice versa - For each unit increase in X2 (Wins), Y (Winnings) will increase by $13544.81, and vice Free Trial versa - For each unit increase inGetX330(Topdays5), Yof(Winnings)freePremiumwillincrease by $71629.39, and vice versa - For each unit increase in X4 (Top 10), Y (Winnings) will increase by $117070.57, and vice versa Test for individual significance: Already Premium? Log in - Checking the individual significance helps us determine whether the independent variables (Poles, Wins, Top 5, Top 10) have an impact on the dependent variable (Winnings) or not - This can be achieved by performing a t-test at the significance level Here, we consider α = 05, and this test is conducted individually for each variable - t30, 025 = 2.042 + Variable X1 (Poles) Hypotheses: H0: =0 (no linear relationship) H1: (linear relationship does exist between X1 and Y) t1 = We have: t30, 025 > => Accept H0 *Conclusion: There is not evidence that Poles affect Winnings at α= 05 + Variable X2 (Wins) Hypotheses: H0: =0 (no linear relationship) H1: (linear relationship does exist between X2 and Y) t2 = We have: t30, 025 > => Accept H0 *Conclusion: There is not evidence that Wins affect Winnings at α= 05 + Variable X3 (Top 5) Hypotheses: H0: =0 (no linear relationship) H1: (linear relationship does exist between X3 and Y) t3 = We have: t30, 025 > => Accept H0 *Conclusion: There is not evidence that Top affect Winnings at α= 05 + Variable X4 (Top 10) Hypotheses: H0: b4=0 (no linear relationship) H1: b40 (linear relationship does exist between x4 and y) Test statistic t30, 025 = 2.042 t4 = We have: t30, 025 < => Reject H0 *Conclusion: There is evidence that Top 10 affect Winnings at α= 05 Problem Assuming that: Y: dependent variable Winnings X1, X2, X5, X6: independent variables Poles, Wins, Top 2-5, Top 6-10 We have the regression equation: Winnings (Y) = 3140367.09 -12938.92* X1 + 202244.78* X2 + 188699.97* X5 + 117070.57* X6 From this regression equation, we can draw the following conclusions: - When the variable X1 (Poles) increases by 1, Y (Winnings) decreases by $12938.92, and vice versa - When the variable X2 (Wins) increases by 1, Y (Winnings) increases by $202244.78, and vice versa - When the variable X5 (Top 2-5) increases by 1, Y (Winnings) increases by $188699.97, and vice versa - When the variable X6 (Top 6-10) increases by 1, Y (Winnings) increases by $117070.57, and vice versa Test for individual significance - Testing the individual significance helps us determine whether the independent variables (Poles, Wins, Top 2-5, Top 6-10) have an influence on the dependent variable (Winnings) or not - This can be achieved by conducting a t-test at a significance level of α = 0.05 Each variable is tested individually - Test statistic: t30, 025 = 2.042 + Variable X1 (Poles) Hypotheses: H0: =0 (no linear relationship) H1: (linear relationship does exist between X1 and Y) Test statistic t30, 025 = 2.042 This is a preview Do you want full access? Go Premium We have: t30, 025 > => Accept H0 t= and unlock all 19 pages *Conclusion: There is not evidence that Poles affect Winnings at α= 05 Access to all documents + Variable X2 (Wins) Hypotheses: HGet0:=0 Unlimited(nolinearrelationship)Downloads H1: (linear relationship does exist between X2 and Y) Improve yourt2grades= We have: t30, 025 < => Reject H0 *Conclusion: There is evidence that Wins affect Winnings at α= 05 X Upload + Variable (Top 2-5) Hypotheses: H0: =0 (no linear relationship) Share your documents to unlock H1: (linear relationship does exist between X5 and Y) t5 = We have: t30, 025 < => Reject H0 *Conclusion: There is evidence FreethatTopTri2-5alffect Winnings at α= 05 + Variable X6 (Top 6-10) Hypotheses: Get 30 days of free Premium H0: =0 (no linear relationship) H1: (linear relationship does exist between X6 and Y) t6 = We have: t30, 025 < =>AlrRejeady ctH0 Premium? Log in *Conclusion: There is evidence that Top 6-10 affect Winnings at α= 05 Problem In regression model from question (including Poles, Wins, Top 5, Top 10), only one independent variable, Top 10, is significant in explaining the dependent variable, Winnings In regression model from question (including Poles, Wins, Top 2-5, Top 6-10), three variables, Wins, Top 2-5, and Top 6-10, are significant in explaining the variable Winnings → Therefore, the regression model from question 3: Winnings (Y) = 3140367.09 - 12938.92 * X1 + 202244.78 * X2 + 188699.97 * X5 + 117070.57 * X6 will be better used to predict Winnings