Which of the following reasons can be used to justify statement #3 in the proof?
1 answer:
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Answer:
So the answer for this case would be n=159 rounded up to the nearest integer
Step-by-step explanation:
Assuming this complete question: A union of restaurant and foodservice workers would like to estimate the mean hourly wage, , of foodservice workers in the U.S. The union will choose a random sample of wages and then estimate using the mean of the sample. What is the minimum sample size needed in order for the union to be 95% confident that its estimate is within $0.35 of ? Suppose that the standard deviation of wages of foodservice workers in the U.S. is about $2.15 .
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
represent the sample mean for the sample
population mean (variable of interest)
represent the population standard deviation
n represent the sample size
Solution to the problem
Since the Confidence is 0.95 or 95%, the value of The margin of error is given by this formula:
(a)
And on this case we have that ME =0.35 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025;0;1)", and we got , replacing into formula (b) we got:
So the answer for this case would be n=159 rounded up to the nearest integer
Answer:
For better understanding of the answer see the attached figure :
length of grid square on each axis on coordinate plane is 1 units
But here it is given to be 0.1 units.
So, in order to find the ordered pair (1.8 , -1.2) we need to first locate 1.8 on x-axis and -1.2 on y-axis
Now, as each axis one grid square equals 0.1 . So,we go 18 units on positive x -axis and mark point (1.8,0) and 12 units on negative y-axis and mark point (0,-1.2) and draw vertical and horizontal lines passing through these points respectively. And the point of intersection of these lines is our required point (1.8,-1.2)
