N a packing plant, one of the machines packs jars into a box. A sales rep for a packing machine manufacturer comes into the plant saying that a new machine he is selling will pack the jars faster than the old machine. To test this claim, each machine is timed for how long it takes to pack 10 cartons of jars at randomly chosen times. Given a 99% confidence interval of (-8.6, -3.08) for the true difference in average times to pack the jars (old machine - new machine), what can you conclude from this interval?

After replace we got for the interval:

For this case since the interval have just negative values then we can conclude that at 1% of significance the mean for the old case is lower than the mean for the new machine and for this case we can conclude that the new machine reduce the times to pack the jars.

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

For this case we assume the following:

represent the man for old case

represent the man for new case

deviation for the old case

deviation for the new case

For this case we want to find a confidence interval for the difference of means and they can use the following formula:

After replace we got for the interval:

For this case since the interval have just negative values then we can conclude that at 1% of significance the mean for the old case is lower than the mean for the new machine and for this case we can conclude that the new machine reduce the times to pack the jars.

answer:

it is general formula that is used to write value to its excet position

a11 a12 a13

a21 a22 a23

it is the example of order 2 by 3 matrix in this

a11 means value occur in 1 st row 1st column

a12 means value occurs in 1st row 2nd column

a13 means value occur in 1st row and 3rd column

a21 means value occurs in 2nd row and 1st column

a22 means value occurs in 2nd row and in 2nd column

a23 means value occurs in 2nd row and in 3rd column

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.