Solve the following question by using R language
You run an experiment and collect the following measurements:
21.3 20.1 16.5 21.5 10.7 17.4 18.5 18.7 19.0 20.5 20.6 9.1 16.7 5.5 20.4 12.0
1. Measure the sample mean, the sample median, the sample standard deviation, the sample 20th percentile, the sample geometric mean, and the sample harmonic mean.
2. Produce a normal quantile-quantile plot using the data and use an appropriate statistical test to assess if the data are sampled from a normal distribution (be sure to include a p-value). If the data are not normal, use one sentence to describe in what manner the distribution deviates from normal.
3. Calculate 95% confidence intervals on the population mean, population median, population standard deviation, population 20th percentile, population geometric mean, and population harmonic mean using a bootstrap in R. (For full credit, use the pivot/empirical bootstrap or the Studentized bootstrap.)
4. A hypothesis states that 20% of the population from which the data were sampled should have values less than 15. Can you rule this out? Explain, and show any calculations. 5. Another hypothesis states that no more than 5% of the population should have values less than
5. Can you rule this out? Explain, and show any calculations.