Question

Researchers presented a study of the wear out failure time of used colored display panels purchased by an outlet store (Mathematical Sciences Colloquium, December 2001). Prior to acquisition, the panels had been used for about one-third of their expected lifetimes. The failure times (in years) for a sample of 50 used panels are reproduced and saved in PANELFAIL file. Find a 95% confidence interval for the true mean failure time of used colored display panels.

FailTime Withdrawal

0.01 No

1.21 No

1.71 No

2.30 No

2.96 No

0.19 No

1.22 No

1.75 No

2.30 No

2.98 No

0.51 No

1.24 No

1.77 No

2.41 No

3.19 No

0.57 No

1.48 No

1.79 No

2.44 No

3.25 No

0.70 No

1.54 No

1.88 No

2.57 No

3.31 No

0.73 No

1.59 No

1.90 No

2.61 No

1.19 No

0.75 No

1.61 No

1.93 No

2.62 No

3.50 No

0.75 No

1.61 No

2.01 No

2.72 No

3.50 No

1.11 No

1.62 No

2.16 No

2.76 No

3.50 No

1.16 Yes

1.62 Yes

2.18 Yes

2.84 Yes

3.50 Yes

Answer 1

Answer:

Given that,

Researchers presented a study of the wear out failure time of used colored display panels purchased by an outlet store (Mathematical Sciences Colloquium, December 2001).

Prior to acquisition, the panels had been used for about one-third of their expected lifetimes.

The failure times (in years) for a sample of 50 used panels are reproduced and saved in PANELFAIL file.

Find a 95% confidence interval for the true mean failure time of used colored display panel:

We can find the sample mean and sample standard deviation of the given data set using excel function =AVERAGE( ) and =STDEV.S( ) respectively.

Therefore = 1.935 , S = 0.9287, n = 50

Population standard deviation σ is unknown therefore we use T interval.

Confidence interval is given by,

Lower bound = – E

Upper bound = + E

Margin of error ; t is critical value follows t distribution with degrees of freedom (d.f ) = n - 1

We have n = 50 and confidence level (c) = 95% or 0.95

d.f = n-1 = 50-1 = 49

α = 1 – c = 1- 0.95 = 0.05

We can find critical value t using excel function =TINV(α,d.f)

=TINV(0.05,49) = 2.01

Therefore ,

Margin of error =( 2.01 0.9287)/ V50

Margin of error E = 0.2640

Lower bound = – E = 1.935 - 0.2640 = 1.671

Upper bound = + E = 1.935 + 0.2640 = 2.199

95% confidence interval for the true mean failure time of used colored display panels is ( 1.671, 2.199).