Question

A large school district in Connecticut wants to estimate the average SAT score of this year's graduating class using a 95% confidence interval. The district takes a simple random sample of 100 seniors. The sample mean is 510 and the population standard deviation for SAT scores is known to be 75. What is the 95% confidence interval for µ?

Answer 1

Answer:

[ 502.5, 517.5]

Step-by-step explanation:

Given:

Mean of the sample, µ = 510

Total sample size, n = 100

Standard deviation = 75

Confidence level = 95%

Now,

The interval for µ is given as:

⇒ µ ± $z\frac{\sigma}{\sqrt n}$

for 95% confidence level z value = 1.96

Thus,

The interval for µ

⇒ 510 ± $1.96\times\frac{75}{\sqrt{100}}$

or

⇒ 510 ± 7.5

or

⇒ [ 510 - 7.5, 510 + 7.5 ]

or

⇒ [ 502.5, 517.5]