find the unknown number in the following proportion. round your answer to the nearest hundredths if necessary check your answer
by finding the cross products
1 answer:
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Answer:
a: 1037 is the minimum sample size needed
b: 712 is the minimum sample size needed
Step-by-step explanation:
We need to use the formula for minimum sample size of a proportion when a sample proportion is known.
The level of confidence is 99%, which has a corresponding z-value of 2.575.
We know the desired error is 4%, or 0.04.
Part a: We have no prior estimate. See attached photo for calculation
Part b:
We know p-hat = 0.22. Therefore q-hat = 1 - 0.22 = 0.78
See the attached photo for the calculation of the minimum sample size
Answer:
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 circuits that show evidence of undercutting is significantly less than 0.05.
Step-by-step explanation:
1) Data given and notation
n=1000 represent the random sample taken
X=33 represent the number of circuits that show evidence of undercutting
estimated proportion of circuits that show evidence of undercutting
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 they reduce the rate of undercutting to less than 5%.:
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 left 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 circuits that show evidence of undercutting is significantly less than 0.05.