use the following to solve a, b, c,d, e,f and g below) th Question #4 ( rking fo
ID: 3312493 • Letter: U
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use the following to solve a, b, c,d, e,f and g below) th Question #4 ( rking for a leading electronics firm claims to have invented a An engineer wo lasting TV picture tubes. Tests run on s50 picture tubes made wi 1,600 hours. Tests the old process consistently show a mean life of 1,538 hour made with the new process show a mean life run over the last three years on a very large number of TV an life of 1,538 hours and TV picture tubea i o a standard deviation of 136 hours. a) What is the sampling distribution of xbar, and how do suming the claim is true, how likely was it to have gotten a mean of 1,600 from sample? b) As your If you would like to test whether the engineer's work has produced a picture tube that definite longer, what would be... ly lasts c).the null hypothesis? d) .the alternative hypothesis? el) .the test statistic? f) the critical value? (Use = 0.05) 8) the result of the significance test? Note: BE THOROUGH. Do NOT just answer Reject or Fail to Reject.Explanation / Answer
a.
By Central limit theorem, the sampling distribution xbar is a normal distribution with mean as population mean and standard deviation as population standard deviation divided by square root of number of samples.
b.
Mean of sample mean = 1538
Standard deviation of sample mean = 136 / sqrt(50) = 19.23
P(X = 1600) = P[Z = (1600 - 1538) / 19.23] = P[Z = 3.22] = 0.0022
c.
Null hypothesis H0: The sample mean is 1538 hrs.
d.
Alternative hypothesis Ha: The sample mean is greater than 1538 hrs.
e.
z = (1600 - 1538) / 19.23 = 3.22
f.
critical value for significance level of 0.05 is P(z > 0.95) = 1.64
g.
As, observed test statistic (3.22) is greater than the critical value (1.64), we reject the null hypothesis and conclude that sample mean is greater than 1538 hrs.
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