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

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Physics

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.

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

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