Statistics for Business 200032 - Data Set 182 Assignment

This document presents a comprehensive solution to a Statistics for Business assignment, specifically addressing data set 182. The assignment covers key statistical concepts, including calculating a 95% confidence interval for employee overtime using a t-value due to the unknown population standard deviation. It proceeds with hypothesis testing, first assessing whether the average employee age exceeds 30, utilizing a t-test and comparing the p-value to a significance level. The solution then examines the claim that average salaries of male and female employees are the same, employing a two-sample independent t-test for equal variance, and concluding based on the p-value relative to the significance level. Finally, it investigates the relationship between an employee's job type and gender using a chi-square hypothesis test, determining if there is a significant association based on the p-value and significance level. The solution demonstrates proficiency in applying statistical methods to real-world business scenarios and interpreting the results.

COMPUTER ASSIGNMENT
DATA SET: 182
STUDENT ID:
[Pick the date]

DATA SET: 182
Question 1
95% confidence interval for overtime of employee work needs to be determined.
It is apparent that population standard deviation is not given and hence, t value would be
taken into account in place of z value.
It can be said with 95% confidence that the mean amount of overtime that employees work
for each week would fall within the interval 4.24 hours and 6.26 hours.
Question 2
Hypothesis testing
Claim: Average employee is older than 30 years old.
It is apparent that population standard deviation is not given and hence, t value would be
taken into account in place of z value.
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It can be seen from the above that the significance level is 1% and the obtained p value is
0.0618. Clearly, the p value is higher than the significance level and hence, insufficient
evidence is present to reject the null hypothesis and to accept the alternative hypothesis.
Therefore, it cannot be said that the average employee is older than 30 years old.
Question 3
Hypothesis testing
Claim: Average salary of male employees is same as the average salary of female employees.
It is apparent that population standard deviation is not given and hence, t stat would be used
here. Further, we have two samples which are independent in nature and also, it is given that
the unknown population standard deviation of salary of male employees and female
employees are same and therefore, the appropriate test would be two sample independent t
test for equal variance.
Null hypothesis H0 :μmale=μfemale
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Alternative hypothesis Ha : μmale ≠ μfemale
The given level of significance = 0.05
It is a two tailed hypothesis test as evident from the sign of the alternative hypothesis.
Thereby, the two tailed p value would be used here. It can be seen that the two tailed p value
comes out to be 0.0327 which is lower than the level of significance. Therefore, sufficient
evidence is present to reject null hypothesis and to accept alternative hypothesis. Hence, the
conclusion can be made that the average salary of males is not same as the average salary of
female employees.
Question 4
Significance level = 0.05
Whether Job Type of an employee is related to gender or not.
The most appropriate test is chi square hypothesis test.
Null hypothesis H0 :Job Type of an employee is not related ¿ gender
Alternative hypothesis Ha :Job Type of an employee is related ¿ gender
Chi square hypothesis test
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The given level of significance = 0.05
It can be seen that the p value comes out to be 0.0264 which is lower than the level of
significance. Therefore, sufficient evidence is present to reject null hypothesis and to accept
alternative hypothesis. Hence, the conclusion can be made that Job Type of an employee is
significantly related to gender.
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