Question

The amount of time until a laptop breaks down follows a an exponential distribution which has the following distribution

F(x) =        1 – exp(- ?x),         if x ≥ 0

0                   ,     otherwise

The parameter ?=1, the population mean and standard deviations are equal to 1/?. A sample size of n = 32 was generated from the above population distribution for k = 10,000 times. One of these samples 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.

1. For each of the 10,000 samples, a sample mean can be calculated, state (with reasons) the distribution of these sample means.
2. By applying the Central Limit Theorem, calculate the mean and the standard deviation of the sample means (show your final answer correct to four decimal places).
3. Based on the Sample Dateset X, perform a hypothesis testing on the population mean ? = 1 (the significance level ? = 0.05).

Answer 1