Statistics Frequency Drawing of Histogram

Question: Discuss about the Statistics Frequency for the Drawing of Histogram. Answer: 1: The data records the body temperatures of males and females. The body temperature of males and females are assumed to be normal. The mean body temperature is calculated on the basis of the given sample data and a confidence interval for the mean value is calculated. First of all, one has to test whether the distribution that is assumed to be normal in the problem, really a normal distribution or not. The normality can be checked by different methods. The most common method is drawing Histogram of the data. The histogram of body temperatures is given below: Figure: Histogram of body temperatures (Source: Created by author) The above figure shows the histogram of normal body temperature. The distribution is approximately normal. The normal body temperature is classified into two groups males and females. In general, the body temperature of male differs from that of females. Therefore one should at first test whether there is a significant difference between the means of the two distributions or not. Therefore, the hypothesis is to test, H0: 1 = 2 against H1: inequality in H0. The statistic for the test is t = ((x1bar-x2bar) - (1 - 2))/s. The value of the test statistic is -2.28. The p-value of the test statistic is 0.01, which is rejected at 5% level of significance. Therefore, the male and female population differs in terms of body temperatures. Therefore, in order to detect whether a patient has a normal body temperature, separate confidence intervals for male and the female population needs to be calculated. The confidence interval for normal body temperature of the males is: I = (x-bar 1.96 * s/) I = (36.4297, 37.02014) The confidence interval for the female population is given by the following formula: I = (x-bar 1.96 * s/) C.I = (36.55164, 37.22006). The normal body temperature for males should lie between (36.4297,37.02014) and the normal body temperature for female should lie between (36.55164, 37.22006). However, as per these results at 95% confidence interval, the confidence interval for normal body temperature came out to be (36.7347, 36.8760). As per this result, the mean body temperature of male and female lies outside the confidence interval, which depicts that 95% confidence interval, is not a fit for the model. The mean value of normal body temperature is 36.8054. The confidence interval for the mean at 99% confidence interval for both male and female together came out to be (36.71200, 36.89876). The mean body temperature of males and females are 36.724 and 36.885 according to our sample data lies in this confidence interval for normal body temperature. On the other hand, this depicts that 99% confidence interval suits the model than 95% confidence interval. 2: The p-value for the t test with significance level 0.05 suggests that the test would be rejected. Therefore, the level of significance for this test could not be 0.5. The level of significance needs to be lowered in order to accept the test. There are two types of errors associated in any testing problem. One is type I error and the other is Type II error. The type I error occurs when null hypothesis is accepted when it is false and Type II error occurs when the null hypothesis is rejected when it is true. The following table gives the type I error and type II errors. Null hypothesis true Null hypothesis false Reject H0 Type I error Correct Accept H0 Correct Type II error In order to get a good test one need to reduce both the errors. But it is not possible to reduce both the error probabilities at the same time. One can reduce one error probability at the cost of increasing the other error probability. The Type I error probability involves rejection of the null hypothesis when it is true. Therefore, the rejection of null hypothesis when it is true is more serious than accepting the hypothesis when it is true. The Type I error has to be reduced as much as possible in order to get a better test.