Question

Fifty specimens of a new computer chip were tested for speed in a certain application, along with 50 specimens of chips with the old design. The average speed, in MHz, for the new chips was 495.6, and the standard deviation was 19.4. The average speed for the old chips was 481.2, and the standard deviation was 14.3.Can you conclude that the mean speed of the new chips is greater than that of the old chips?

Answer 1

Under 99% confidence level we can say that mean speed of the new chips is greater than that of the old chips

Explanation:

`H_(0)`: Mean speed of the new chip is the same as the old chip

`H_(a)`: Mean speed of the new chip is greater than the old chip

to calculate the z-statistic we can use the formula:

z=
`\frac{M_(n)-M_(o)}{\sqrt{(s_(n)^2)/(N_(n)) +(s_(o)^2)/(N_(o)) } }`

if we put the numbers then

z=
`\frac{495.6-481.2}{\sqrt{(19.4^2)/(65)} +(14.3^2)/(65) } }` =4.8171

The probability of this z-statistic is < 0.001 Therefore Under 99% confidence level we can say that mean speed of the new chips is greater than that of the old chips