statistic

MA 320-8A

The 95% and 99% confidence interval are shown in the range of a data set. This range of values shows that the chances that population means can lie in this range of interval.

Calculate confidence intervals for the quantitative variables in the Heart Rate Dataset. In the Heart Rate Dataset, we have two qualitative variables as the male and female heart rate. These two variables are categorized into two groups in which males denoted as 0, and the female is denoted as 1. The heart rate took before as resting and after exercise of the person. Here we are calculating the z-score of the data. It shows the data which calculate the standard deviations from the mean. The z-score calculating by the formula given by, z = (x – μ) / σ

Here, we have the sample of size n= 150, which is then, from the overall population size of the given data is 200, and the male population is 108, and the female population is 92. The community follows a normal distribution. We are taking this range of delivery to calculate the one sample population. By using the data tool, we have got the value of the sample mean is 15. The estimated standard deviation is 2. Now, we have calculated the z- scores, and we have taken a hypothetical mean value where μ=15. This is exactly equal to the sample mean of the data received.

So, the calculated Z score value is 0, which shows that the benefits are exact average. By calculating we get the value of the standard error 0.1633. Here we have the table for the confidence intervals of the z-score at 95% and 99% level of confidence intervals.

In the table, we have calculated the two-tailed test we get the lower and the upper limits of the confidence intervals. At the 95% level, the value of the Z score is 1.96 and at the 99% level, the value is 2.576. The 95 % confidence interval for the mean is (15.32, 14.68) and 99% level of the confidence interval for the mean is (15.42, 14.58).

 Now again, we are considering two samples. First sample with the size 40 and second sample with the size 50. By using the data tool, we have got the value of the sample mean of the first sample is 50 and the value of the mean of the second sample is 51. The differences between the two means are of value 1. The standard deviation of the first sample is 1.2 and the standard deviation of the second sample is 1.8. By solving the given data, we get the z-score -163.7846. Also from the table, we get the value of the standard deviation of 0.317. The hypothetical difference between the two samples 51. So here the difference between the sample value and the hypothetical value is -52. Here, from the table the calculated standard error.

Here we have the table for the confidence intervals of the z-score at 95% and 99% level of confidence intervals. The z- score value at 95% and 99% is 1.96 and 2.576. The 95 % confidence interval for the mean is (-0.378,-1.622) and 99% level of the confidence interval for the mean is (-0.182,-1.818).