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.

If we compare the p value obtained and the significance level given we have 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

estimated proportion of chips do not fail in the first 1000 hours of their use

is the value that we want to test  

represent the significance level  

Confidence=99% or 0.99  

z would represent the statistic (variable of interest)  

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:  

Alternative hypothesis:  

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

(1)  

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

3) Calculate the statistic  

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

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 . The next step would be calculate the p value for this test.  

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

If we compare the p value obtained and the significance level given we have 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%.  

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

answer: i wpould go with c

step-by-step explanation: