Probability and Statistics for Engineering

Question: Discuss about the Probability and Statistics for Engineering. Answer: Introduction: A historical data on the birth weight of babies has been obtained from a Local Health District in 2002. The data has been obtained by simple random sampling. The data contains birth weight of the babies born (in gms) along with the age, height, weight, smoking habit and the gestation period of the females. The data has been analyzed using various statistical tools and techniques. A histogram diagram has been obtained for the weight of the babies. The data has been at first converted into a frequency data. The histogram diagram has been obtained by plotting the mid value of the weight of babies along the x axis and the frequency along the y axis. The histogram diagram shows that the distribution of the weight of the babies cannot be assumed to be normally distributed. The histogram shows a negatively skewed distribution. The summary statistical measure for the weight of the babies has been calculated for analysis. It has been found that the mean value of the distribution is 3354.517 while the median value is 3374. The mean and the median are the measures of central tendencies. The measures give an idea about the central value of the distribution. The standard deviation of the measure is 461.8166. The standard deviation measures the deviation from the central values. The standard deviation is not very large for the dataset. The skewness value for the variable bwt is -0.44301. The variable bwt has a negatively skewed distribution. The minimum value of the bwt is 2013 while the maximum value is 4309. The range is the difference between the maximum and minimum observations. The entire set of observations lies within the range. The range is a very crude and the easiest measure of dispersion. The proper measure is the standard deviation. The standard deviation actually gives the average squared deviation f rom the mean value of the observation. The mode is another measure of central tendency. The mode is that observation which occurs most frequently in the dataset. The modal value for this dataset is 2948. The mean, median values agree closely for this dataset. The central or average value of the dataset is expected to lie within 3354 and 3374. The confidence interval has also been calculated for the mean value. The confidence interval is an interval within which the estimated value of the mean is expected to lie even if the sample is change. The random sample is expected to come from a population. If the sample observations are changed then the estimate of the mean value is also expected to change. Then the mean value will lie within the calculated interval. The confidence interval has been calculated to be (3269.583, 3439.451). The report has been analyzed to get an idea about the average body weight of the babies. The average body weight of the babies is found to be around 3374. The body weight o the babies is negatively skewed. The idea about the mean body weight of the babies born in a Local Health District has been calculated. The main objective of the report is to use summary statistics measure to get a crude idea about the distribution of the weight of the babies. The weight of the babies has been found to follow a negatively skewed distribution. The skewness value is calculated to be -0.44301. The skewness value is however much less almost approaching towards 0 value. This may be due to the presence of outliers. The outliers of the distribution have to be detected with the help of some statistical methods such as scatter plot. The mean value has been calculated with the help of the sample observation. The sample is derived from a particular population. The sample may vary. The variation of sample will give different values of the mean, median and other measures. In order to get an idea about mean, an interval has been calculated. The value of arithmetic mean is expected to lie within the interval. The interval has been calculated assuming a normal distribution whereas the body weight of babies does not follow normal distribution. Therefore, the calculation of the interval is not appropriate for this case. The body weight of the babies is dependent on various factors. The body weight of the babies may depend on the age of mother, weight, height and other habits of the mother. The report aims to analyze the average body weight of the babies. The number of aged mothers who are giving birth to the babies and the average weight of the babies are being calculated for the purpose of analysis. The women who are giving birth to the babies are of different age. The mothers who are above the age 35 are being calculated. A sample of size one hundred and sixteen has been obtained for the purpose of the study. The sample has been obtained by the method of simple random sampling procedure. In the sample chosen, sixteen mothers are found to be above the age 35. The estimated proportion has been calculated to be 16/116 = 0.137931. The confidence interval is calculated by the following formula: I = (p sqrt(p*(1-p)/n) * 1.96, p + sqrt(p*(1-p)/n)*1.96) Therefore, the proportion of mother who is above the age 35 is not very large. The confidence interval for the estimated value is ( 0.075179, 0.200683). The average weight of the babies according to European heritage is expected to be 3.5 kg. A test has been conducted to test this claim. The average weight of the babies in the sample has been found to be 3355. A t-test has been conducted for the sample. The null hypothesis of the test is H0: = 3500 against H1: 3500. The statistic of the test has been calculated to be -2.97682. The degrees of freedom of the t-distribution are 115. The tabulated value of t is 1.984. Therefore, the null hypothesis of the test is accepted. The average weight of the babies in the district can be assumed to be 3.5 kgs. Conclusion: The report gives an idea about the average weight of the babies born in a Local Health District. The inferential statistical techniques are being calculated to get an idea about the average weight of babies born to the mother. The number of mothers born above the age 35 is being estimated in this report. A t-test has been conducted to know about the average weight of the babies. It has been found on the basis of the test that the average weight of the babies can be assumed to be 3.5 kilograms Bibliography: Ang, S., Van Dyne, L. (2015).Handbook of cultural intelligence. Routledge. Devore, J. L. (2015).Probability and Statistics for Engineering and the Sciences. Cengage Learning. Gravetter, F. J., Wallnau, L. B. (2016).Statistics for the behavioral sciences. Cengage Learning. Lowry, R. (2014). 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