Population Distributions - statistics lab report Essay

Population Distributions - statistics lab report - Essay Example This theory is based on the concept that a heart with small size will have smaller cardiac output as compared to the larger heart. Hence, this scientific theory proposes that the heart beat of the larger individual will beat slowly to meet the metabolic requirements. The above hypothesis will be examined by collecting a sample of short and tall individuals and identify whether there are significant differences in their heart beat rates. To prove this, an experiment will be conducted which will find out whether there are considerable differences in the heart rate of tall and short subjects. The experts in the field8 as have also emphasized that individuals who are physically fit have a higher stroke volume as compared to inactive individuals. This means that individuals having a poor physical condition will reach their maximum heart beat rate at a lower work level than individuals who are physically fit. Based on the above belief, a theory has been put forward that since physically fi t individuals have a higher aerobic capacity before reaching maximum heart rate therefore they will have a slower rate of increase in heart beat and a faster return to the resting return after the exercise. For the verification of aforementioned hypothesis, a controlled experiment will be conducted in which the subject’s heart rate before exercise and 15 minutes after exercise and then 30 minutes after exercise will be measured to know whether there are significant differences in the heart rate of individuals in the group. Null Hypothesis 1: Measurement of heart rate. Analysis of the data: a) Number of Subjects in each class Range Frequency 40-50 0 50-60 3 60-70 10 70-80 19 80-90 8 90-100 2 >100 0 b) Histogram Figure 1: Histogram of Heart Beats per Minute Median = 76 Mode = 80 Both the median and mode lie in the 70-80 subject group of the variable. c) The data for the given variable is spread symmetrically around the central location. It has a modal class. I expect the data t o be modal since most of the individuals will have a common heart beat rate with few exceptional cases. My expectations are supported by the graph of histogram as majority of the frequency of the data lies in the middle of set. d) Null Hypothesis: (There is no difference in the mean heart rate of the tall and short subjects) Alternative Hypothesis: (There is a difference in the mean heart rate of the tall and short subjects) Significance Level The hypothesis is to be performed at 5% significance level or 95% confidence level, so Critical Value The critical values for the two tailed test for with confidence level of are If the value of the t test statistic is lesser than -2.02 or greater than 2.02 than reject; otherwise do not reject. T-test Value: The data values for the small subject group and tall subject group are attached in the appendix (Table 1 and Table 2) Where By using formulas we calculate that (All the calculations are given in appendix) Where The value of t-test statisti c is -0.339 and it does not fall in the rejection region thus we do not reject the null hypothesis. The test results are not statistically significant at the 5% level; that is, at the 5% significance level, the data do not provide sufficient evidence to conclude that there is difference in the mean heart rate of the tall and short individuals. Null Hypothesis 2 and 3: Heart rate and recovery after exercise. a) Mean heart rate These are the class mean heart rates (beats per minute) Before Exercise 75.2 Directly After Exercise 124.8 After 1 Minute 105.9 After 5 Minutes