Mathematics, 10.12.2019 04:31 Fuunn326

Asample of 1600 computer chips revealed that 60% of the chips do not fail in the first 1000 hours of their use. the company's promotional literature claimed that above 57% do not fail in the first 1000 hours of their use. is there sufficient evidence at the 0.01 level to support the company's claim? state the null and alternative hypotheses for the above scenario.

Answers: 3

Show answers

Answers

If we compare the p value obtained and the significance level given $\alpha=0.01$ we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 1% of significance the proportion of chips that do not fail in the first 1000 hours of their use is significantly higher than 0.57 or 57%.

Step-by-step explanation:

1) Data given and notation

n=1600 represent the random sample taken

X=0.6*1600=960 represent the number of chips do not fail in the first 1000 hours of their use

$\hat p=\frac{960}{1600}=0.6$ estimated proportion of chips do not fail in the first 1000 hours of their use

p_o=0.57 is the value that we want to test

$\alpha=0.01$ represent the significance level

Confidence=99% or 0.99

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that above 57% of chips do not fail in the first 1000 hours of their use :

Null hypothesis: $p\leq 0.57$

Alternative hypothesis: p 0.57

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 .

3) Calculate the statistic

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

$z=\frac{0.6 -0.57}{\sqrt{\frac{0.57(1-0.57)}{1600}}}=2.42$

4) 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 $\alpha=0.01$ . 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(z2.42)=0.0078

Answer from: Quest

answer: its because of life

step-by-step explanation: i dont know

Answer from: Quest

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 13:40

1234567891011 match the reasons with the statements in the proof. given: j | | k m 1 = m 3 prove: l | | m 1. j||k, m∠3 = m∠1 if lines are ||, then corresponding angles are =. 2. m∠1 = m∠2 if alternate interior angles are =, then lines are ||. 3. m∠2 = m∠3 substitution 4. l||m given

Answers: 3

Answer

Mathematics, 21.06.2019 19:00

Can someone me out here number 4 plz

Answers: 1

Answer

Mathematics, 21.06.2019 20:00

Someone answer asap for ! max recorded the heights of 500 male humans. he found that the heights were normally distributed around a mean of 177 centimeters. which statements about max’s data must be true? a. the median of max’s data is 250 b. more than half of the data points max recorded were 177 centimeters. c. a data point chosen at random is as likely to be above the mean as it is to be below the mean. d. every height within three standard deviations of the mean is equally likely to be chosen if a data point is selected at random.

Answers: 1

Answer

Mathematics, 21.06.2019 20:30

Which expression is equivalent to (4 +6i)^2? ? -20 + 48i 8 + 12i 16 - 36i 20 + 48i

Answers: 1

Answer

You know the right answer?

Asample of 1600 computer chips revealed that 60% of the chips do not fail in the first 1000 hours of...

Questions

Mathematics, 02.02.2021 19:10

7. ALGEBRA Sara Allen is interested in buying a notebook computer. If she buys the computer this week, she will save $150.00 while it is marked down 1...