Question

The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 53.9 for a sample of size 24 and standard deviation 5.6. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 90% confidence level). Assume the data is from a normally distributed population. Enter your answer as a tri-linear inequality accurate to three decimal places.
_______ < μ < _________ please teach using calculator method

Answer 1

Answer:

The  estimate is

             $52.02 < \mu < 55.78$

Step-by-step explanation:

From the question we are told that

    The sample mean is $\ = x = 53.9$

     The sample size is  n =  24

      The standard deviation is  $\sigma = 5.6$

 

Given that the confidence level is  90% the level of significance is mathematically represented as

           $\alpha = 100 - 90$

            $\alpha = 10 \%$

            $\alpha = 0.10$

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

           $Z_{\frac{\alpha }{2} } =Z_{\frac{0.10 }{2} } = 1.645$

The reason we are obtaining critical value of    $\frac{\alpha }{2}$ instead of    $\alpha$ is because    $\alpha$

represents the area under the normal curve where the confidence level interval (  $1 - \alpha$ ) did not cover which include both the left and right tail while  

$\frac{\alpha }{2}$ is just the area of one tail which what we required to calculate the margin of error

NOTE: We can also obtain the value using critical value calculator (math dot armstrong dot edu)

Generally the margin of error is mathematically represented as

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

substituting values

         $E = 1.645 * \frac{5.6 }{ \sqrt{24} }$

          $E = 1.880$

The  estimate of how much the drug will lower a typical patient's systolic blood pressure(using a 90% confidence level) is mathematically represented as

         $\= x - E < \mu < \= x + E$

substituting values

         $53.9 - 1.880 < \mu < 53.9 + 1.880$

         $52.02 < \mu < 55.78$