SOLUTION: A random sample of 15 students majoring in computer science has an average SAT score of 𝑥̅ = 1173 with a standard deviation of 𝑠 = 85. Let x be a random variable representin

Question 1171912: A random sample of 15 students majoring in computer science has an average SAT score of 𝑥̅ = 1173 with a standard deviation of 𝑠 = 85. Let x be a random variable representing the SAT score for all computer science majors. Assume the distribution of x is mound shaped and symmetric. Previous studies indicate that the average SAT score for computer science major was about μ = 1143. Find a 90% confidence interval for the population average SAT score μ of all computer science majors. Truncate to two decimal places. What does the confidence interval mean in the context of this problem?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The 90% half-interval is t(0.95,df=14)*s/sqrt(n)
this is 1.761*85/sqrt(15)=38.65
the 90% CI is then (1134.35, 1211.65)
Because mu was 1143, and mu lies within the CI, there is no evidence that the results obtained are due to a change in the mean, or that there is now a new distribution with a new mean. Said another way, we would fail to reject Ho. We are highly confident (90%) that the true mean lies within this interval.
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