SOLUTION: From a random sample of 70 high school seniors in a particular school district , the mean and standard deviation of the verbal scores in the scholastic Aptitute Test (SAT) are foun

Question 1051565: From a random sample of 70 high school seniors in a particular school district , the mean and standard deviation of the verbal scores in the scholastic Aptitute Test (SAT) are found to be 433 and 47, respectively. Based on this sample, construct a 98 % confidence interval for the mean verbal score in the SAT for the population of all seniors in this school district.
Thank you
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Our first step is to calculate the Margin of Error(ME)
:
Since we know the standard deviation of the statistic, we use the following
:
ME = critical value * standard deviation of the statistic
:
Since our sample size is > 30, we use the normal distribution and our critical
value is the z-score
:
Next, calculate alpha
:
alpha(a) = 1 - (confidence level / 100) = 0.02
:
critical probability(p^*) = 1 - (a/2) = 0.99
:
the z-score associate with p^* is 2.32
:
Therefore ME = 2.33 * 47 = 109.51
:
************************************************************
Our 98% confidence interval(CI) = sample statistic + or - ME
:
CI = 433 + or - 109.51 = (323.49, 542.51)
************************************************************
:
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