(Tiểu luận) business statistics

Problem 2 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

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Trường Đại học Kinh tế Quốc dân

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BUSINESS STATISTICS

Group 6

Name

:

Nguyễn Trần Nhật

Anh Nguyễn Thị Mai

Anh Trương Minh

Ánh Nguyễn Công

Bách Lê Ngọc Hải Vũ

Kiều Trang Vũ Thu

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MSV: 11219023 MSV: 11219021 MSV: 11219032 MSV: 11219033 MSV: 11219055 MSV: 11219141 MSV: 11219143

Hà Nội – 06/2023

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I CHAP 12

1 Problem 1

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

2 Problem 2

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:

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From the above screenshot, the Uploadstatisticsis10.19

The P-value is 0.0061

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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. Free Trial

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.

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From the above screenshot, the statistics is 3.72 The

P- value is 0.1557

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

4 Problem 4

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

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From the above screenshot, the statistics is 5.11

The P- value is 0.0776

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

5 Problem 5

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

1 Problem 1

*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 3 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:

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Thus, the descriptive statistics forUploadtheyearsofexperience and salary for individuals employed in outside sales positions is obtained

Output using EXCEL is given asSharefollows:your documents to unlock

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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

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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

*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

< µ <

Output using EXCEL software is given below:

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The 95% confidence interval for the mean is:

62,966.41 < µ < 66,884.55 Thus, the 95% confidence interval estimate of the mean annual salary for sales persons regardless of year of experience and type of position is (62,966.41, 66,884.55)

3 Problem 3

Calculation:

From part (1), the mean salary for the inside sales based on low, medium and high is given below:

The overall mean salary for inside sales person is provided below:

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55,093.17 < µ < 56,947.87 Thus, the 95% confidence intervalImproveestimateyourofthe gradesmensalary for inside sales persons is (55,093.17, 56,947.87)

4 Problem 4

*Calculation:

Upload

The 95% confidence interval for the mean salary for outside salesperson is,

< µ <

The mean and standard deviation for salary of outside sales persons are ,

Here,

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The 95% confidence interval for the mean is:

< µ <

Access to all documents The 95% confidence

interval for the mean is:

Substitute , , innthe above formula:

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< µ <

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Thus, the 95% confidence interval estimate of the mean salary for inside sales persons is (, )

5 Question 5

By EXCEL software, we have the output given below:

From the EXCE L output, the F-ratio is 251.54 and the

0.000 Decision:

If p-value ≼ ⍺ , reject the null hypothesis H₀

If the p-value ≻ ⍺ fails to reject the null hypothesis H₀

*Conclusion:

Here, the p-value is less than the level of significance

That is, p-value (=0.000) < ⍺ (=0.05 )

Therefore, the null hypothesis is rejected

There is sufficient evidence to conclude that there is a significant difference in the mean of positions at ⍺ = 0.05 level of significance

6 Problem 6

Output using the EXCEL software is given below:

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From the EXCEL output, the F-ratio is 7.93 and the p-value is 0.001.

*Conclusion:

That is, p-value (=0.001) < ⍺ (=0.05 )

In conclusion, there is sufficient evidence to conclude that there is a significant difference in the mean of positions at ⍺ = 0.05 level of significance

7 Problem 7

The output obtained by the EXCEL procedure is as follows:

For Factor A (Position), the F-test statistic is 751.36 and the p-value is 0.000

For Factor B (Experience), the F-test statistic is 65.86 and the p-value is 0.000

For interaction, the F-test statistic is 53.38 and the p-value is 0.000

Decision:

If p-value ≼ ⍺ , reject the null hypothesis H₀

If the p-value ≻ ⍺, fails to reject the null hypothesis H₀

*Conclusion:

Factor A:

That is, p-value (= 0.000 ) < ⍺ (=0.05)

That is, the main effect of factor A (Position) is significant

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Factor B:

That is, p-value (= 0.000 ) < ⍺ (=0.05)

Access to all documents Therefore, the null hypothesis is rejected

That is, the main effect of factor B (Experience) is significant

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That is, p-value (= 0.000 ) < ⍺ (=0.05)

Thus, the interaction is significant

1 Problem 1

Assume Y: dependent variable Winnings

X1, X2, X3, X4: independent variables Poles, Wins, Top 5, Top 10

To determine among these four variables, which variable provides the best single prediction of winnings,

we have a tool called theFreecofficientTrialofdetermination (R Square) The variable with the highest R Square can be considered as the variable that provides the best prediction of winnings

- The influence of the independent variable Poles (X1) on the dependent variable Y.

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We see R Square = 0.1649 => Independent variable X1 explains 16.49% of the variation

in the dependent variable or this linear regression model is appropriate for the amount of X1 data at 16.49%

- The influence of the independent variable Wins (X2) on the dependent variable Y.

- The influence of the independent variable Top 5 (X3) on the dependent variable Y.

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- The influence of the independent variable Top 10 (β4) on the dependent variable Y.

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

2 Problem 2

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We obtain the regression equation:

Winnings (Y) = 3140367.087Upload-12938.92×X1 + 13544.81×X2 +

71629.39×X3 + 117070.57×X4

From this regression equation, we can draw some conclusions:

- For each 1 unit increase in X1 (Poles), Y (Winnings) will decrease by $12938.92, and vice versa

- For each 1 unit increase in X2 (Wins), Y (Winnings) will increase by $13544.81, and vice versa

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- For each 1 unit increase inGetX330(Topdays5), Yof(Winnings)freePremiumwillincrease

by $71629.39, and vice versa

- For each 1 unit increase in X4 (Top 10), Y (Winnings) will increase by $117070.57, and vice versa

Test for individual significance:

- 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

+ Variable X1 (Poles)

Hypotheses: H0: =0 (no linear relationship)

H1: 0 (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

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+ Variable X2 (Wins)

t2 =

*Conclusion: There is not evidence that Wins affect Winnings at α= 05

+ Variable X3 (Top 5)

t3 =

*Conclusion: There is not evidence that Top 5 affect Winnings at α= 05

+ Variable X 4 (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

3 Problem 3

Assuming that: Y: dependent variable Winnings

X1, X2, X5, X6: independent variables Poles, Wins, Top 2-5, Top 6-10

Tiêu đề	Business Statistics
Tác giả	Nguyễn Trần Nhật Anh, Nguyễn Thị Mai Anh, Trương Minh Ánh, Nguyễn Công Bách, Lê Ngọc Hải, Vũ Kiều Trang, Vũ Thu Trang
Trường học	Trường Đại học Kinh tế Quốc dân
Thể loại	Essay
Năm xuất bản	2023
Thành phố	Hà Nội

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