Question

You are testing 0:=100 against :<100 based on an SRS of 24 observations from a normal population. The data gives ¯=9 and =2.4 . What is the value of the statistic? Provide your answer with precision to two decimal places.

Answer 1

Answer:

-185.75297

Step-by-step explanation:

Solution:-

- We are testing whether the population mean u is equal to 100 as per claim.

                Null hypothesis: u = 100

- Where a alternate hypothesis suggest that the population mean ( u ) may be lower:

               Alternate hypothesis: u < 100

- We are given sample data parameters which are assumed to be normally distributed:

              sample mean, x_bar = 9

              sample standard deviation, s = 2.4

- A sample of n = 24 observation was taken from a population of ( N ) with unknown population standard deviation ( σ ).

- The conditions of standard normal distribution are no longer applicable i.e:

                 

              n = 24 < 30

              unknown population standard deviation ( σ )

- We will model the sample using t-distribution with ( n - 1 ) = 23 degrees of freedom.

- The t-statistics of the sample mean x_bar can be determined from standard t-distribution:

                 

                 $t-test = \sqrt{n}* \frac{x_b_a_r - u}{s} \\\\t-test = \sqrt{24}* \frac{9 - 100}{2.4} \\\\t-test = -185.75297$

- The t-test value for mean ( u ) is -185.75297