Batteries R Us is a manufacturer of batteries and are testing a new production technique for their most popular battery type. It is known that the mean lifetime of these batteries made using the previous production technique was 69 hours. The standard deviation in battery lifetime is 5.0 hours and it is assumed that this has not changed. They would like to know whether mean battery lifetime has increased with the new production technique. The following sample data of battery lifetimes has been collected from a random sample of 40 batteries made using the new manufacturing technique. Battery lifetimes (hours)
82.5 78.4 80.2 78.7 67.8 76 74.8 73.9 68.8 70.3 70.7 70.7 77.9
80.5 73.8 80.979.2 74.173.2 76.1 69 73 70.9 63.3 67.8 78.5 68.7
67.5 68.2 68.2 73.3 75.4 73.2 72.2 72.6 72 71.3 69.9 69.6 70.4

Required:
a. Conduct a hypothesis test to test whether the new manufacturing process has increased mean battery lifetime.
b. Calculate the test statistic.

(a) Accept the alternate hypothesis

(b)

Step-by-step explanation:

Given

The sample data

Solving (a): Test whether the process increases the mean battery life

First, we state the null hypothesis

This states that the mean is 69

Next, the alternate hypothesis is to test that the mean has changed.

i.e

Calculate the mean:

Calculate the standard deviation

From the calculations above: The calculated mean 73.0875 is not the same as 69.

Hence, we accept the null hypothesis that:

Solving (b): The test statistic

This is calculated as:

This gives:

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.