Question

The average daily volume of a computer stock in 2011 was ų=35.1 million shares, according to a reliable source. A stock analyst believes that the stock volume in 2014 is different from the 2011 level. Based on a random sample of 30 trading days in 2014, he finds the sample mean to be 32.7 million shares, with a standard deviation of s=14.6 million shares. Test the hypothesis by constructing a 95% confidence interval. Complete a and b A. State the hypothesis B. Construct a 95% confidence interval about the sample mean of stocks traded in 2014.

Answer 1

Answer:

a

   The  null hypothesis is  $H_o : \mu = 35 .1 \ million \ shares$

    The  alternative hypothesis  $H_a : \mu \ne 35.1\ million \ shares$

b

 The   95% confidence interval is  $27.475 < \mu < 37.925$

Step-by-step explanation:

From the question the we are told that

      The  population mean is  $\mu = 35.1 \ million \ shares$

      The  sample size is  n = 30

       The  sample mean is  $\= x = 32.7 \ million\ shares$

       The standard deviation is  $\sigma = 14.6 \ million\ shares$

     

Given that the confidence level is  $95\%$ then the level of significance is mathematically represented as

                  $\alpha = 100-95$

                  $\alpha = 5\%$

=>               $\alpha = 0.05$

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

    The value is  $Z_{\frac{\alpha }{2} } = 1.96$

Generally the margin of error is mathematically represented as

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

substituting values

                $E = 1.96 * \frac{ 14.6 }{\sqrt{30} }$

                $E = 5.225$

The 95% confidence interval confidence interval is mathematically represented as

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

substituting values

               $32.7 - 5.225 < \mu < 32.7 + 5.225$

                $27.475 < \mu < 37.925$