35. In a simple random sample of 25 high school students, the sample mean of the SAT scores was 1450, and the sample variance was 900. Assume that the data come from a normal distribution , a 95.4 % Confidence interval for the population mean is a. 1450 +/- 180 b. 1450 +/- 18 c. 1450 +/- 12 d. 1450 +/- 360

And the best option would be:

c. 1450 +/- 12

Step-by-step explanation:

Information provided

represent the sample mean for the SAT scores

population mean (variable of interest)

represent the sample variance given

n=25 represent the sample size  

Solution

The confidence interval for the true mean is given by :

  (1)

The sample deviation would be

The degrees of freedom are given by:

The Confidence is 0.954 or 95.4%, the value of and , assuming that we can use the normal distribution in order to find the quantile the critical value would be

The confidence interval would be

And the best option would be:

c. 1450 +/- 12