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    Math Problem
  • Level:
    High School
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Question One

  1. The Weekly-Ordinary-Time-Salary

Summary indicators

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The average-weekly-ordinary-time-salary for the personnel is $873.42. However, most of the workers receive an approximate salary of $530.00. The median salary earned by the employees is $742.50. From the box plot, the portions of the wage box–plot are not equal which indicates that the salary is not well distributed. The longer upper whisker shows that the salary varies most towards the positive quartile.

The histogram shows a better distribution of the wages for the forty-eight employees. Most of the employees receive a pay between $400 and $550. The number of the employees reduced as the number of wages increased up to $1250. However, between $1250 and $1600, the number of staff greater and finally decreased between $1600 and $1800. The data is skewed to the left.

  1. A similar study for gender, managers, and non-managers, three levels of job security.

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a. Multiple ways exist. The smallest value is shown

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There is no gender balance among the employees, but there is an excellent job positions distribution. Regarding job security, there is a right balance, but the majority of the workers lie in employment level of safety 2.

Question 2: Job satisfaction for the 48 employees

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The lowermost level of job contentment is 8, while the uppermost level of job contentment is 18. Only one employee has the highest level of satisfaction, and two employees have the lowermost level of job contentment. The majority of employees have a job satisfaction of 17.

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The box plot has a longer lower whisker, which clearly shows that job satisfaction varies mostly in the negative quartile. The sections of the box plot are uneven, indicating that job satisfaction among the employees is changing.

Question 3: Scatter Diagrams

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The WkSalary and EducYrs has a near-zero correlation. However, the relationship is positive as indicated by the value of R2, which is both active and weak (statistics 13).

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There exists a positive correlation and high between WkSalry and AtConrobar. The line has a positive gradient, and the R2 is both confident and vigorous.

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There exists near zero correlation between Pretty and AtConrobar.

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There exists a weak correlation between UOvTime and Age.

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There exists a weak correlation between the Prdtvty and WkSalry.

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The relationship between DysAbsnt and Age is weak.

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The correlation between Prdvty and DysAbsnt is nonlinear.

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The relationship between WkSalry and Age is both active and healthy.

Question 4:

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From the Levene’s test of variance, the significance value is greater than 0.05. Therefore, we use the first column to determine if there is statistically important variance between the means. The two-tailed significant level is 0.041, which is less than 0.05. Therefore, we conclude that there is a difference in the average of gender and education years. The box plots below shows that there is a difference between the medians of sex and teaching years.

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Question 5: Days Mentioned and Days Absent

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From the clear case above and the box plot, the average number of the women who were late is higher compared to the average number of men who were late.

Question 6: (a) Estimate of mean productivity for all employees

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(b) Estimate of the mean productivity of the females and males

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(c) To the significant level of the Leven’s Test equality of variance is 0.275, which is greater than 0.05. Therefore, we must use the first column to determine whether there exists a statistically viable difference in the average productivity of the females and males. The two-tailed significance level has the value 0.054, which is greater than 0.05. Therefore, we conclude that there exists no statistically significant difference in the average productivity of the female and male employees.

(d) Sample size for the margin of error of 10

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Question 7: Age

  1. The mean age (confidence interval 95%)

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Mean age is 36.46 years

  1. Mean age of managers and non-managers

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The mean age for managers is 34.50 years, while that of the non-managers is 38.42.

The significance level of Levene’s test for equality is 0.052, which is more than 0.05. Therefore, we use the first column to determine if there is any difference in the mean age (Field, 2013). The two-tailed significance level is 0.240, which is also greater than 0.05. Therefore, there is no significant difference in the mean age between the age of the managers and non-managers.

Question 8: Hypothesis Testing

Null Hypothesis
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Alternative Hypothesis
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The significance level from the test is equal to zero, which clearly shows that we must reject the null hypothesis and accept the alternative hypothesis. Therefore, the mean age of the Conrobar workers is not forty-five. Therefore, the mean average of workers from industries similar to Conrobar is also not 45 year. From the one test, the mean average is 36.46 years.


Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics. Boston: SAGE.