There is a need to create a 95% confidence interval of the number of calories in chocolate chip cookies of normal size based on a sample of 9 cookies from different bakeries. The sample has a mean of 75 calories and a sample standard deviation, s, of 27.3. Please Interpret the results so I could understand how to do it.

Answer

75 + or -  20.98

Upper limits  =  75 + 20.98 =  95.98

Lower limits  =  75 - 20.98  =  54.02

95% confidence interval   =  [ 54.02 , 95.98]

Interpretation

We are 95%  confident that the true population mean  of the number of calories in chocolate chip cookies  is between  54.02 to  95.98   

Step-by-step explanation

Explanation

Data

Sample size  n =  9

Sample mean  x? = 75

Sample standard deviation s = 27.3

A  95% confidence interval of the number of calories in chocolate chip cookies   is calculated as follows;

   Sample  mean  x?  + or -  95% confidence level t critical  value  with  n-1 degrees of freedom x Standard error

  We use  Student's t test  since sample size n is  smaller  that is  n< 30  and  population standard deviation is unknown.

Sample  mean  x? = 75

95% confidence level t critical  value  with  n-1 degrees of freedom =  t_{0.05/2 , n-1}  =  t_{0.025, 8} = From t distribution table t critical value = 2.306

 Standard error  =  s/?n

                           = 27.3/ ?9

                            = 27.3/3

                            =  9.1

95% confidence interval will be;

x? + or - 2.306 x 9.1

75 + or -  20.98

Upper limits  =  75 + 20.98 =  95.98

Lower limits  =  75 - 20.98  =  54.02

95% confidence interval   =  [ 54.02 , 95.98]

Interpretation

We are 95%  confident that the true population mean  of the number of calories in chocolate chip cookies  is between  54.02 to  95.98