Statistic question

Question

A small pilot study was conducted prior to planning a large research study investigating the average SAT-verbal scores of students at one large high school. In the sample mean was 688 with a standard deviation of 116. Researchers want to construct a 95% confidence interval to estimate the mean in the population of all students at this school with a margin of error of +- 10. What is the minimum sample size they should ontain? Use a z multipler of 1.960.

Answer 1

Relevant formulas

Margin of Error= Z_Crit×σ/sq rt(n)

Step 1: State Your Givens:

σ = 116

Z_Crit = 1.960

X = 688

E = ±10

Step 2: Work through the Relevant Formula

Margin of Error= Z_Crit×σ/sq rt(n)

10 = 1.960 × 116 / sq rt(n)

**We want to get n by itself**

n = ((Z_Crit × σ)/E)²

n ⁼ ((1.960 × 116)/10)²

n = 516.93

n ≈ 517

The minimum sample size needed for this pilot study is 517.

I hope this helps. If you have any additional questions, feel free to reach out to me.

Take care,

-Dr. C