Respuesta :
Given Confidence interval is 80% and we are only using 1 sample.
First find degrees of freedom = sample size - 1
Or: df = 26-1 = 25
Now subtract confidence int by 1 and divide by two to make it two tailed. Remember normal distribution looks bell-shaped and we are only looking on one side for our CI.
So: (1-0.8)/2= 0.2/2=0.1 which is our alpha
Now we need to use T-distribution table that should be found in textbook or online.
For 25 df and an alpha of 0.1 I get 1.316.
Some t-dist tables will even have the confidence intervals given DF on the bottom.
Now we have to divide sample Standard deviation by sample size to find the Standard error. This basically is to look for SD of all sample means around population mean, but more on that can be found online.
So: se= 46.5/sqrt(26)
Se= 9.119 let’s call it 9.12
Now multiply standard error by value from t-dist table: 9.12*1.316 = 12.0019 let’s call it 12.
So now to find confidence interval of 80% subtract to find lower bound and add to find upper bound from given mean.
Upper: 305.3 + 12 = 317.3
Lower: 305.3 - 12 = 293.3
First find degrees of freedom = sample size - 1
Or: df = 26-1 = 25
Now subtract confidence int by 1 and divide by two to make it two tailed. Remember normal distribution looks bell-shaped and we are only looking on one side for our CI.
So: (1-0.8)/2= 0.2/2=0.1 which is our alpha
Now we need to use T-distribution table that should be found in textbook or online.
For 25 df and an alpha of 0.1 I get 1.316.
Some t-dist tables will even have the confidence intervals given DF on the bottom.
Now we have to divide sample Standard deviation by sample size to find the Standard error. This basically is to look for SD of all sample means around population mean, but more on that can be found online.
So: se= 46.5/sqrt(26)
Se= 9.119 let’s call it 9.12
Now multiply standard error by value from t-dist table: 9.12*1.316 = 12.0019 let’s call it 12.
So now to find confidence interval of 80% subtract to find lower bound and add to find upper bound from given mean.
Upper: 305.3 + 12 = 317.3
Lower: 305.3 - 12 = 293.3
