Amanufacturer of nickel-hydrogen batteries randomly selects 100 nickel plates for test cells, cycles them a specified number of times, and determines that 14 of the plates have blistered.

(a) does this provide compelling evidence for concluding that more than 10% of all plates blister under such circumstances? state and test the appropriate hypotheses using a significance level of .05. in reaching your conclusion, what type of error might you have committed?

(b) if it is really the case that 15% of all plates blister under these circumstances and a sample size 100 is used, how likely is it that the null hypothesis of part (a) will not be rejected by the 0.05 test? answer this question for a sample size of 200.

(c) how many plates would have to be tested to have \(\beta(.15)\) = 0.10 for the test of part (a)?

Step-by-step explanation:

Test the claim about a single population proportion where the null hypothesis is of the form of {H_0}:p = {p_0}H  

The formula for single proportion is,

Here, pp denote the population proportion

Let be the number of successes in a sample of size.

Let be the total sample size.

a)

Null hypothesis,

Alternative hypothesis,

Level of significance,

Decision Rule: Reject

Calculate the test statistic value.

Calculate the p−value of the test.

(b)

It is really case that 15% of all plates blister under these circumstances and a sample size of 100 is used.

Hence, the probability that will not be rejecting using the  is 0.4927.

Therefore, there is 49.27% of all samples will result in correct rejection of null hypothesis

For the sample size n = 200,n=200, the probability of type-II error is calculated as follows:

(c)

The number of plates is,

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

it is not that hard all u have to do is plot the graph

step-by-step explanation: