Mathematics, 21.02.2020 04:30 hailey5129

A fellow-student calculates a 99% confidence interval for a mean and gets (0.020,0.045). She says that there is a 99% chance that the true mean is between 0.020 and 0.045. Is she right? Why or why not?

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No. Once the confidence interval is calculated, the probability that it contains the true mean is either 1 or 0. So then is not appropiate says that the confidence level is a chance. The best conclusion for this case would be:

We have 99% confidence that the true mean for the variable of interest on this case is between (0.02; 0.045)

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".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

After apply the procedure we got that the interval is (0.02; 0.045) and we need to analyze if the following conclusion is right or no:

She says that there is a 99% chance that the true mean is between 0.020 and 0.045. Is she right? Why or why not?

The best answer for this case would be:

We have 99% confidence that the true mean for the variable of interest on this case is between (0.02; 0.045)

Answer from: Quest

Ibelieve its 0 but i am not sure

Answer from: Quest

c - they will have the same distribution

step-by-step explanation:

this is the only one that could make sense. : )

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A fellow-student calculates a 99% confidence interval for a mean and gets (0.020,0.045). She says th...

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