1. It is believed that the average level of prothrombin in the blood of a normal population is 20 mg with a standard dev

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1. It is believed that the average level of prothrombin in the
blood of a normal population is 20 mg with a standard deviation of
4 mg. To verify this, a sample is taken from 40 individuals in whom
the average is 18.5 mg. Can the hypothesis be accepted with a
significance level of 5%?
2. The life span of light bulbs manufactured by a GE
follows a normal distribution with a standard deviation of 120
hours. GE claims that the average life is at least 800
hours. You would like to test if the GE claim is true.
At random, a sample of 50 bulbs from a lot is selected and it is
revealed that the average life is 750 hours. With a significance
level of 0.01, should the lot be rejected by not honoring the
warranty?
3. A company that packages peanuts states that at a
maximum 6% of the peanut shells contain no nuts. At random, 300
peanuts were selected and 21 of them were empty.
With a significance level of 1%, can the statement made by the
company be accepted?
4.) The left Twix machine and the right Twix machine have been
adding an unknown about of vitamin B into their candy bars.
The owner of the plants has done a study of both machines.
81 random bars produced by the left Twix machine had the sample
average .0020 ounces of vitamin B with a sample standard deviation
of .001 ounce.
64 random bars produced by the right Twix machine had the sample
average .0017 ounces of vitamin B with a sample standard deviation
of .0003 ounce.
With a significance level of 5%, test the null hypothesis that
both machines insert the same amount of vitamin B into their
bars.