Mathematics, 18.04.2020 03:50 sabrinaunderhillx

A computer manufacturer is testing a batch of processors. They place a simple random sample of processors from the batch under a stress test and record the number of failures, their guidelines specify the percentage of failures should be under 4%. Of the 300 processors tested, there were 54 failures.

a. State the hypotheses for the test. Assume the manufacturer wants to assume there is a problem with a batch, that is, they will only accept that there are fewer than 4% failures in the population if they have evidence for it.

b. Calculate the test statistic and p-value. Your test statistic should be either a z-value or a t-value, whichever is appropriate for the problem

Answers: 2

Show answers

Answers

Answer from: Aggie9595

a)We need to conduct a hypothesis in order to test the claim that the true proportion is lower than 0.04 or no.:

Null hypothesis: $p \leq 0.04$

Alternative hypothesis: p 0.04

When we conduct a proportion test we need to use the z statistic, and the is given by:

b) We need to use a z statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.135 -0.04}{\sqrt{\frac{0.04(1-0.04)}{300}}}=8.396$

Since is a right tailed test the p value would be:

$p_v =P(z8.396) \approx 0$

Step-by-step explanation:

Data given and notation

n=400 represent the random sample taken

X=54 represent the number of failures

$\hat p=\frac{54}{400}=0.135$ estimated proportion of adults that said that it is morally wrong to not report all income on tax returns

p_o=0.04 is the value that we want to test

$\alpha$ represent the significance level

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)

Part a: Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion is lower than 0.04 or no.:

Null hypothesis: $p \leq 0.04$

Alternative hypothesis: p 0.04

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value p_o .

Part b: Calculate the statistic

We need to use a z statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.135 -0.04}{\sqrt{\frac{0.04(1-0.04)}{300}}}=8.396$

Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.05$ . The next step would be calculate the p value for this test.

Since is a right tailed test the p value would be:

$p_v =P(z8.396) \approx 0$

So the p value obtained was a very low value and using the significance level for example $\alpha=0.05$ we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of defectives is significantly higher than 0.04 or 4%

Answer from: Quest

the mean and mad

step-by-step explanation:

Answer from: Quest

range is infinite on both x and y axis positive and negative

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 16:30

Jorge planted flowers in his garden he planted one row of 12 tulips and one row of 36 daisies george's friend kylie has a garden with 75 flowers in it kylie's garden only contains tulips and daisies. is it possible for kylie‘s garden she have the same ratio of tulips to daisies as george's garden?

Answers: 1

Answer

Mathematics, 21.06.2019 16:50

The lines shown below are parallel. if the green line has a slope of -1, what is the slope of the red line?

Answers: 1

Answer

Mathematics, 21.06.2019 17:40

The perimeter of a rectangle is greater than or equal to 74 meters. if the length is 25 meters, the minimum width of the rectangle is meters.

Answers: 2

Answer

Mathematics, 21.06.2019 19:00

Samantha is growing a garden in her back yard. she spend $90 setting up the garden bed and buying the proper garden supplies. in addition, each seed she plants cost $0.25. a. write the function f(x) that represents samantha's total cost on her garden. b. explain what x represents. c. explain what f(x) represents. d. if samantha plants 55 seeds, how much did she spend in total?

Answers: 2

Answer

You know the right answer?

A computer manufacturer is testing a batch of processors. They place a simple random sample of proce...

Questions