2. A simple of 900 students has mean 3.5 cm and standard deviation 2.61 cm is the sample from a large population of mean 3.25 cm and standard deviation 2.61 cm? Check at 99% level of confidence. Also find the range.

The sample mean is not from a large population with  mean 3.25 cm and standard deviation 2.61 cm

The range is  

Step-by-step explanation:

From the question we are told that

   The  sample  size is  n  =  900

   The  sample  mean is  

    The  standard deviation is  

    The population mean is  

    The  population standard deviation

Given that confidence level is  99% the significance level is evaluated as

The  critical value  of   is obtained from the normal distribution table , the value is

The  null hypothesis  

The  alternative  

Generally the test statistics is mathematically represented

=>  

=>  

The  p-value  is  from the z-table , the value  is  

  So we can see that   so we reject the null hypothesis

Hence the sample mean is not from a large population with  mean 3.25 cm and standard deviation 2.61 cm

Generally the margin of error is mathematically represented as

The range is evaluated as

=>  

=>  

180 square centimeters

step-by-step explanation:

answer: evaluate the objective function at each vertex to determine which - and -values, if any, maximize or minimize the function. example: find the minimum value and maximum value of the objective function f ( x , y ) = 4 x + 5 y , subject to the following constraints