Decision making, quantitative technique, data analysis, sample, probability, population, confidence interval, unknown parameter, estimation, theoretical value, excel formula, age distribution, descriptive statistics, quantitative variables
The population in this example is the number of boys of a certain age. We have a sample of 25 boys of the same age, whose mean weight is 80.94 pounds. It is argued that boys in the neighborhood from which the sample is drawn are underfed. We can observe that there is a difference of almost 5 pounds between the municipal sample and the mean population, but that does not necessarily mean that boys in the neighborhood are underfed. We need to perform a test to check whether the difference of 5 pounds is statistically significant.
[...] Given that it is greater than we reject the null hypothesis that the distribution is random, and conclude that there are significant differences in weight losses between the two drug treatments and the placebo group among men and women. Another test is carried out for those with physical activities and weight losses for all three treatment. The Chi statistic is 0.0985, with a p-value of 95.19% so we reject the null hypothesis that the distribution is random, and that weight losses are uniform across contingencies. [...]
[...] On the Excel sheet we can build the confidence interval using the formula presented above, or use the Excel formula CONFIDENCE which uses the following arguments: the level of confidence - or 95% confidence) the standard deviation (11.6) and the sample size (25). We then add and subtract the obtained value to the sample mean of 80.94 pounds. Question Using data from its candidate pool, company ZTel has concluded that test results are normally distributed with a mean 525 and standard deviation 55. Its past policy was to accept automatically all those candidates whose score is 600 and higher, while rejecting all those candidates who score below 425. [...]
[...] Figure: Age distribution - sample of 32 individuals We can see that the sample is relatively young, as 78% of the individuals are aged 26 and less. The sample is indeed skewed in favour of younger individuals, but that does not show in the summary statistics of the table above because there are some older individuals aged 28-30 that make up partially for the small percentage of individuals aged 26-28. Height and weight distributions are more spread out in comparison to age in the sample. [...]
[...] A drug trial for weight loss is carried out on a sample of 32 individuals. Each one has been given two drugs, type A and type while a control group was given a Placebo. In addition, individuals in the sample also decide to exercise or not during the trial period. We would like to identify which drug has the most effect on weight loss. There are as many men as there are women in this sample, while the Placebo (control) group makes up 37.5% of the sample, the rest is equally divided among drugs A and B. [...]
[...] On average, individuals who exercise lose 2.7kg, whereas those who do not lose 0.72kg, the Student test yields a statistic of 5.793, and an equivalent p-value of less than 1%. We list on the tables below average weight loss per drug treatment group, gender, physical activity for which the previous tests have been carried out. Table: contingency table for drug treatment per physical activity Physical activity DRUG A DRUG B Placebo Total No 0,5 1,2 0,56 0,72 Yes 3,2 3,2 1,33 2,79 Total 2,1 2,2 0,75 1,63 Since there are significant differences in the two contingency tables reported above, we can see that average weight loss for women in the sample is higher with drug whereas drug A is more effective on men. [...]
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