Asked by Kathryn Lockwood on Jul 25, 2024
Verified
A random sample of 81 SAT scores of students applying for merit scholarships showed an average of 1400 with a standard deviation of 300.The t value needed to develop the 95% confidence interval for the population mean SAT score is
A) 1.96.
B) 1.998.
C) 1.645.
D) 1.28.
Confidence interval
A range of values, derived from sample data, that is believed to contain the true value of a population parameter with a certain probability.
SAT scores
Scores resulting from the Scholastic Assessment Test, a standardized test widely used for college admissions in the United States.
- Distinguish the application of standard normal distribution from t-distributions in the context of constructing confidence intervals.
Verified Answer
KS
Kwabena SarpongJul 31, 2024
Final Answer :
B
Explanation :
The correct t value for a 95% confidence interval with 80 degrees of freedom (n-1 = 81-1 = 80) is closer to the value provided in option B, 1.998. This is because for large samples, the t-distribution approaches the z-distribution, but with a sample size of 81, the exact value from the t-distribution should be used, which is typically found in t-tables and is slightly different from the z-value of 1.96 used for the normal distribution.
Learning Objectives
- Distinguish the application of standard normal distribution from t-distributions in the context of constructing confidence intervals.
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