Question

(use the following to solve a, b, c, d, e, f and g below)

An engineer working for a leading electronics firm claims to have invented a process for making longer-lasting TV picture tubes. Tests run on 50 picture tubes made with the new process show a mean life of 1,700 hours.   Tests run over the last three years on a very large number of TV picture tubes made with the old process consistently show a mean life of 1,638 hours and a standard deviation of 195 hours.  

1. What is the sampling distribution of xbar, and how do you know that?
2. Assuming the claim is true, how likely was it to have gotten a mean of 1,700 from your sample?

If you would like to test whether the engineer’s work has produced a picture tube that definitely lasts longer, what would be…

3. … the null hypothesis?
4. …the alternative hypothesis?
5. …the test statistic?
6. …the critical value? (Use α = 0.05)
7. …the result of the significance test?   Note: BE THOROUGH.   Do NOT just answer Reject or Fail to Reject.

Answer 1

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n = 50

Sample mean = 1700

pop. mean = 1638

Stdev = 195

a. Xbar ~ N(1638, 195/sqrt(50)) = N(1638, 27.58)

b. P(X>1700) = P(Z> (1700-1638)/27.58) = P(Z>2.25) = .0123

c.

Ho: Mu <= 1638

d.

Ha: Mu > 1638

e.

test-statistic = 2.25 ( as calculated above)

f. critical value = alpha = .05

g. The conclusion : We reject Ho and conclude that engineer' work has produced a picture tube that definitely lasts longer