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Answer:
So on this case the 90% confidence interval would be given by (12.019;12.181)
And we can conclude at 90% of confidence that the true mean is between (12.019, 12.181) and since the lower limit is higher than 12 we can conclude that the specification is not satisfied
Step-by-step explanation:
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
population mean (variable of interest)
represent the population standard deviation
n=50 represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
(1)
Since the Confidence is 0.90 or 90%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 90% confidence interval would be given by (12.019;12.181)
And we can conclude at 90% of confidence that the true mean is between (12.019, 12.181) and since the lower limit is higher than 12 we can conclude that the specification is not satisfied
Set up the equations to solve for X >0 since the curve goes up to the right
doing that proves that y=log3(x)
the answer is C
see attached picture:
doing that proves that y=log3(x)
the answer is C
see attached picture: