The amount of time until a laptopbreaks down follows a an exponential distribution which has thefollowing distribution
F(x)=       1 – exp(-?x),        if x ≥ 0
0                  ,    otherwise
The parameter ?=1, the population mean and standard deviationsare equal to 1/?. A sample size of n = 32 was generated from theabove population distribution for k = 10,000 times. One of thesesamples is presented in the table below.
2.5689 | 0.7311 | 1.6212 | 0.0021 | 1.3902 | 0.0057 | 0.9763 | 0.7368 |
0.4962 | 1.2702 | 0.4980 | 1.5437 | 0.0326 | 1.6022 | 0.7332 | 0.1098 |
0.0519 | 0.7981 | 0.4978 | 2.0094 | 3.5883 | 0.0847 | 0.3621 | 0.0116 |
2.8394 | 0.0419 | 0.1961 | 0.0584 | 0.2421 | 0.6413 | 1.8856 | 1.5461 |
Please answer the questions below.
- For each of the 10,000 samples, a sample mean can becalculated, state (with reasons) the distribution of these samplemeans.
- By applying the Central Limit Theorem, calculate themean and the standard deviation of the sample means (show yourfinal answer correct to four decimal places).
- Based on the Sample Dateset X, perform a hypothesistesting on the population mean ? = 1 (the significance level ? =0.05).
