Question

In tests of a computer component, it is found that the mean time between failures is 520 hours. A modification is made which is supposed to increase the time between failures. Tests on a random sample of 10 modified components resulted in the following times (in hours) between failures. 518 548 561 523 536 499 538 557 528 563 At the 0.05 significance level, test the claim that for the modified components, the mean time between failures is not equal to 520 hours.

=

Answer 1

Solution:

x	x2
518	268324
548	300304
561	314721
523	273529
536	287296
499	249001
538	289444
557	310249
528	278784
563	316969
∑x=5371	∑x2=2888621

Mean ˉx=∑xn

=518+548+561+523+536+499+538+557+528+563/10

=5371/10

=537.1

Sample Standard deviation S=√∑x2-(∑x)2nn-1

=√2888621-(5371)210/9

=√2888621-2884764.19

=√3856.9/9

=√428.5444

=20.7013

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :  $\mu$  = 520

H_a : $\mu$    $\neq$ 520

Test statistic = t

= (
T
- $\mu$ ) / S / $\sqrt$ n

= (537-520) / 20.70 / $\sqrt$ 10

= 2.597

Test statistic = t = 2.597

P-value =0.0289

$\alpha$ = 0.05  

P-value < $\alpha$

0.0289 < 0.05

Reject the null hypothesis .

There is sufficient evidence to suggest that