Question

(Small sample confidence intervals for a population mean) suppose you are taking a sampling of 15 measurements. you find that x=75 and s =5. assuming normality, the 99% confidence interval for the population mean is:__________

Answer 1

Answer:

The 99% confidence interval is  $71.67 < \mu < 78.33$

Step-by-step explanation:

From the question we are told that

     The sample  size  is  $n = 15$

      The  sample  mean is  $\= x = 75$

        The  standard deviation is  $s = 5$

 Given that confidence is  99%  then the level of significance is mathematically represented as

              $\alpha = 100 - 99$

             $\alpha = 1\%$

             $\alpha = 0.01$

Next we obtain the critical values of  $\frac{ \alpha }{2}$ from the normal distribution table

   The  value is

                  $Z_{\frac{ \alpha }{2} } = 2.58$

Generally the margin for error is mathematically represented as

            $E = Z_{\frac{ \alpha }{2} } * \frac{ s}{ \sqrt{n} }$

=>         $E = 2.58 * \frac{ 5}{ \sqrt{15} }$

=>         $E = 3.3307$

   The  99% confidence interval is mathematically represented as

             $\= x -E < \mu < \= x +E$

=>          $75 - 3.3307 < \mu$

=>          $71.67 < \mu < 78.33$