Running head: CONFIDENCE INTERVAL FOR MEAN SALARY 1 Confidence interval of mean salary for BA degree Name: Daniela Watkins Course: MTH140 May19, 2016 CONFIDENCE INTERVAL FOR MEAN SALARY 2 Introduction We are interested in finding the confidence interval of the mean salary of the employee who has the qualification as BA degree. We will use the confidence level as 90%,95% and 99%.These confidence interval will give the estimate for the population mean salary who has BA degree as major education with the confidence level mentioned above. Research Question The research question includes to calculate the various confidence interval (90%, 95% and 99%) which will be used to give an estimate for the population mean salary having major in BA degree. Data Collection For this research study, it is important to collect the data for finding the average salaries. For the purpose of the data collection, we collect the data for the random sample of size 150 employee from different work places. A random sample is selected by using the stratified random sampling as we consider the different types of industries as a stratum. The population under study is considered as the all employee in the USA who completed their BA degree in accounting. The data is collected for the variables salary and the gender of the employee. The detailed data is given in the appendix section. Statistical Analysis We have to calculate the 90%, 95% and 99% confidence interval for the mean salary of the sample with BA degree. The confidence intervals of the sample is shown below: 90% confidence interval CONFIDENCE INTERVAL FOR MEAN SALARY 95% confidence interval 99% confidence interval 90% confidence interval for male and female separately 95% confidence interval for male and female separately 3 CONFIDENCE INTERVAL FOR MEAN SALARY 99% confidence interval for male and female separately Comparison table for men and women mean salary for men and women Confidence level 90 male,Lower limit 71.05 male,upper limit 79.71 female,lower limit 68.41 female,upper limit 75.75 Difference between limits male 8.66 female 7.34 95 70.2 80.56 67.69 76.47 99 68.49 82.87 66.27 77.89 10.36 8.78 14.38 11.62 4 CONFIDENCE INTERVAL FOR MEAN SALARY 5 Satandard deviati on of mean salary after BA degree 2 1.5 1 0.5 0 -0.5 -1 -1.5 -2 Conclusion The 90% confidence interval for the mean annual salary (thousands of dollars) after BA degree is between (70.69, 76.25).The male mean annual salary is between (71.05, 79.71) and for the female, it is between (68.41, 75.75). The 95% confidence interval for the mean annual salary (thousands of dollars) after BA degree is between (70.15, 76.79).The male mean annual salary is between (70.2, 80.56) and for the female, it is between (67.69, 76.47). The 99% confidence interval for the mean annual salary (thousands of dollars) after BA degree is between (69.08, 77.85).The male mean annual salary is between (68.49, 82.27) and for the female, it is between (69.08, 77.85). The margin of error for the various confidence interval does not vary too much the data mean salary has low standard deviation. We can also say the data is more distributed around the mean. CONFIDENCE INTERVAL FOR MEAN SALARY 6 The male mean annual salary has more deviation than the female mean annual salary. It is clear from the difference between the upper limit and lower limit at the given confidence level. The difference is greater for male as compared to the female. As the confidence interval overlaps for the male and female, we can say that there is an equality of pay for male and female employee for BA degree. The standard deviation line chart also confirms the fact that almost all the mean annual salary lies between the 2 standard deviation from the mean. So, we can say that 95% and 99% confidence interval should include all the data. References Brenson, M.L. &Levine, D.M. (1999).Basic business statistics: Concepts and applications. Upper Saddle River, NJ: Prentice-Hall Guide to statistical interpretation of data. Confidence interval. (1981).London: British Standard Institution. Johnson, R. &Kuby, P. (2000).Elementary statistics. Pacific Grove: Duxbury. Appendix The data set for this research study is given as below: CONFIDENCE INTERVAL FOR MEAN SALARY No. Annual salary $ 7 Gender CONFIDENCE INTERVAL FOR MEAN SALARY 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 99 67 98 41 82 70 41 50 89 77 78 103 100 58 86 48 97 91 91 44 85 41 89 54 48 90 105 62 89 84 64 83 66 63 77 91 74 54 79 57 53 92 91 84 8 1 1 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 0 0 1 0 0 1 0 1 0 1 1 0 0 1 0 1 CONFIDENCE INTERVAL FOR MEAN SALARY 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 86 80 63 101 49 88 55 76 81 67 92 57 89 54 95 47 79 62 43 64 72 98 79 77 104 105 97 107 84 40 93 104 68 76 107 75 93 60 102 49 79 48 104 44 9 1 0 1 0 0 1 1 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 CONFIDENCE INTERVAL FOR MEAN SALARY 10 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 104 53 95 49 60 99 91 65 47 59 44 45 92 41 81 68 96 49 73 42 66 96 48 58 49 62 60 63 100 106 78 88 43 55 100 91 103 47 47 45 53 58 96 0 0 0 1 0 0 0 0 0 1 0 0 1 1 1 0 1 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 0 0 1 1 0 1 1 0 0 1 CONFIDENCE INTERVAL FOR MEAN SALARY 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 52 104 92 90 63 71 59 41 49 53 80 45 106 53 85 80 86 62 106 11 0 1 0 0 1 0 0 1 0 0 0 1 1 1 1 1 1 0 0