A low-noise transistor for use in computing products is being developed. It is c
ID: 3256324 • Letter: A
Question
A low-noise transistor for use in computing products is being developed. It is claimed that the mean noise level will be below the 2.5-dB level of products currently in use. Tt is believed that the noise level is approximately normal with a standard deviation of 8. a) Set up the appropriate null and alternative hypotheses for verifying the dam about the noise level. b) A sample of 16 transistors yields a mean of 1.8. Find the p-value for the test. c) Do you think that Ho should be rejected? Why or why not? Justify your answer. d) Explain, in the context of this problem, what conclusion can be drawn concerning the noise level of these transistors. If you make a type I error, what will have occurred? What is the probability that you are making such an error? e) Find a 95% Cl for the mean noise level of the population.Explanation / Answer
given that mean = 2.5 and sd = 0.8
a) Hypothesis
Ho : The mean noise level is not less than 2.5 db
H1 : the mean noise level is less than 2.5 db
b)
mean = 1.8 and n = 16
b ) so the t test can be calculated using the formula
t = (x-mu)/(sd/sqrt(n))
(2.5-1.8)/(0.8/sqrt(16)) = 3.5
now df = n-1 = 16-1 = 15
and at 0.05 alpha and 1 tail test , we check the p value from the t table as 0.0016
c) as the p value is less than 0.05 , hence we reject the null hypothesis in favor of alternate hypothesis
d)
the p value is 0.0016 , hence this means that the probability of conducting a type 1 error is 0.0016 , which is extremely low . If we make a type 1 error , then we would have rejcted the null hypothesis even though it was true.
Hence there is only 0.16% chance that the The mean noise level is not less than 2.5 db .
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