The National Ignition Facility uses 6mm diameter pellets of deuterium (hydrogen with an extra neutron) cooled to 11 Kelvin as targets for it’s laser in an attempt to achieve nuclear fusion. Because of the massive energies involved, the targets must be constructed to a very high degree of accuracy. You sample 22 targets and their diameters are collected and stored in the data table.   round.diametermm..5. 1 5.99869 2 6.00053 3 5.99925 4 6.0009 5 5.9996 6 6.00188 7 6.00187 8 6.00091 9 5.99903 10 5.99889 11 6.00037 12 5.99907 13 6.00012 14 6.00114 15 5.99867 16 5.99962 17 5.99989 18 6.00147 19 6.0017 20 6.00153 21 6.0007 22 6.0018 a) State a null an an alternate hypothesis to test the claim that the target manufacturing process isperforming to specifications. (b) Conduct a hypothesis test to with an α = 0.01 to test your hypothesis (c) What sample size would be needed to reliably, with a probability of 80% or better, detect a deviation of 0.001mm from our null hypothesis?

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The National Ignition Facility uses 6mm diameter pellets of deuterium (hydrogen with an extra neutron) cooled to 11 Kelvin as targets for it’s laser in an attempt to achieve nuclear fusion. Because of the massive energies involved, the targets must be constructed to a very high degree of accuracy. You sample 22 targets and their diameters are collected and stored in the data table.

  round.diametermm..5.
1 5.99869
2 6.00053
3 5.99925
4 6.0009
5 5.9996
6 6.00188
7 6.00187
8 6.00091
9 5.99903
10 5.99889
11 6.00037
12 5.99907
13 6.00012
14 6.00114
15 5.99867
16 5.99962
17 5.99989
18 6.00147
19 6.0017
20 6.00153
21 6.0007
22 6.0018

a) State a null an an alternate hypothesis to test the claim that the target manufacturing process isperforming to specifications.
(b) Conduct a hypothesis test to with an α = 0.01 to test your hypothesis
(c) What sample size would be needed to reliably, with a probability of 80% or better, detect a deviation of 0.001mm from our null hypothesis?

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