(i) The air in a “clean room” used for the production of electronic devices is cleaned by filtering. The air on the outside of the filters is monitored daily to check that ambient conditions are not changing significantly. The table below shows the results of counting the number of dust particles in a standard volume of air over a period of time:

Number of particles in sample / Number of samples

0 --> 36

1 --> 42

2 --> 37

3 --> 18

4 --> 5

5 --> 2

>=6 --> 0

If a sample taken at a later date has 8 particles in a standard sample, does it seem that air quality is deteriorating? (Explain your answer, and choice of “test”.)

In my view, i choose student t-test for checking as follow:

The mean of this data set is 200/140= 1.429

• Use two-tailed test. Formulate the null hypothesis and Alternative hypothesis.

H0: μ = μ0, H1: μ ≠ μ0

• Normally use α = 5% , by checking t table, tcrit = 1.980

Then compared t value with tcritic.

But not sure, if this is the optimal method. T^T

(ii) A manufacturer of windows for aircraft has estimated that, prior to the finishing operation, the windows have an average of 4 defects each. After finishing this is reduced to 0.4 defects each.

(a) if the estimate of 4 defects per window was obtained by sampling 125 products. What values would you expect for the Mean and Standard Deviation of this sample?

Based on my understanding, i did like this:

Since the estimation is 4 defects per window, and now there are 125 products total. Therefore, the expected mean of this sample is: E (x) = 4*125= 500. It means we expect there are 500 defects inside this sample.

Apart from this, the data still follows Poisson distribution hence variance equals mean. The expected standard deviation of this sample will be 22.36.

for both two questions, not really sure the optimal answer. Waiting for help to check the best answer.

Thanks for helping!!!

Number of particles in sample / Number of samples

0 --> 36

1 --> 42

2 --> 37

3 --> 18

4 --> 5

5 --> 2

>=6 --> 0

If a sample taken at a later date has 8 particles in a standard sample, does it seem that air quality is deteriorating? (Explain your answer, and choice of “test”.)

In my view, i choose student t-test for checking as follow:

The mean of this data set is 200/140= 1.429

• Use two-tailed test. Formulate the null hypothesis and Alternative hypothesis.

H0: μ = μ0, H1: μ ≠ μ0

• Normally use α = 5% , by checking t table, tcrit = 1.980

Then compared t value with tcritic.

But not sure, if this is the optimal method. T^T

(ii) A manufacturer of windows for aircraft has estimated that, prior to the finishing operation, the windows have an average of 4 defects each. After finishing this is reduced to 0.4 defects each.

(a) if the estimate of 4 defects per window was obtained by sampling 125 products. What values would you expect for the Mean and Standard Deviation of this sample?

Based on my understanding, i did like this:

Since the estimation is 4 defects per window, and now there are 125 products total. Therefore, the expected mean of this sample is: E (x) = 4*125= 500. It means we expect there are 500 defects inside this sample.

Apart from this, the data still follows Poisson distribution hence variance equals mean. The expected standard deviation of this sample will be 22.36.

for both two questions, not really sure the optimal answer. Waiting for help to check the best answer.

Thanks for helping!!!

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