An assembly plant orders a large shipment of electronic circuits each month. the supplier claims that the population proportion of defective circuits is rhoequals0.04. when a shipment arrives, the plant manager selects a random sample of 300 circuits that are tested and the sample proportion of defective circuits is computed. this result is used for a hypothesis test to determine if there is sufficient evidence to conclude that the population proportion of defectives circuits from this supplier is greater than 0.04. the hypotheses are upper h 0: rholess than or equals0.04 and upper h subscript a: rhogreater than0.04.

So the p value obtained was a very low value and using the significance level assumed for example we have 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.  

Step-by-step explanation:

1) Data given and notation  

n=300 represent the random sample taken

X=21 represent the number of defectives (value assumed)

estimated proportion of defectives

is the value that we want to test

represent the significance level

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 the proportion of defectives it's higher than 0.04.:  

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

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

So the p value obtained was a very low value and using the significance level assumed for example we have 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.  

d. 8

step-by-step explanation:

the given radical expression is:

we can rewrite this as:

we express as square numbers to get;

the exponents will now cancel out to give.

the correct answer is d