A 90% confidence interval for the mean has been calculated using a sample size of 21. If the sample size is increased then, all other things

Question

A 90% confidence interval for the mean has been calculated using a sample size of 21. If the sample size is increased then, all other things remaining constant, the confidence interval will become _________.

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Parker 2 weeks 2021-10-03T12:40:07+00:00 1 Answer 0

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    2021-10-03T12:41:17+00:00

    Answer:


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

    \bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}   (1)  

     ME = z_{\alpha/2}\frac{\sigma}{\sqrt{n}}

    And as we can see if we increase the sample size the margin of error would be lower, so then we can conclude that the interval would be narrower respecto to the interval obtained with a sample size of n =21

    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

    \mu population mean (variable of interest)  

    s represent the sample standard deviation  

    n=21 represent the original sample size  

    Calculate the confidence interval


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

    \bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}   (1)  

     ME = z_{\alpha/2}\frac{\sigma}{\sqrt{n}}

    And as we can see if we increase the sample size the margin of error would be lower, so then we can conclude that the interval would be narrower respecto to the interval obtained with a sample size of n =21

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