Question

You want to know if high-school females score differently than high-school males on a standardized test. You take a random sample of 28 males and 27 females from high schools across the country and record their scores. Which confidence interval would you use to analyze these data?

Answer 1

Answer:

$\bar{x_{1}} - \bar{x_{2}} \pm t*\sqrt{s(\frac{1}{n_{1}} + \frac{1}{n_{2}})}$

Step-by-step explanation:

Random sample size of males, n₁ = 28

Random sample size of males, n₂ = 27

Here,

If n₁ < 30 & n₂ < 30,

we use t-distribution

Therefore,

The confidence interval chosen will be

⇒ $\bar{x_{1}} - \bar{x_{2}} \pm t*\sqrt{s(\frac{1}{n_{1}} + \frac{1}{n_{2}})}$

Here,

$\bar{x_{1}}$ is mean of sample n₁

and,

$\bar{x_{2}}$ is mean of sample n₂

s is the standard deviation

the value of 't' can be obtained from the standard t- distribution table