Question

A 97% confidence interval for the mean of a population is to be constructed and must be accurate to within 0.3 unit. A preliminary sample standard deviation is 1.4. The smallest sample size n that provides the desired accuracy is

Answer 1

Answer:

The sample size will be "$102.5494 \sim 102$". A further explanation is given below.

Step-by-step explanation:

Let the sample size will be:

= n

The given values are:

Standard deviation,

= 1.4

ME,

= 0.3

As we know,

⇒ $n=(Z \frac{a}{2}\times \frac{SD}{E})^2$

On putting the estimated values, we get

⇒    $=(2.17\times \frac{1.4}{0 .3})^2$

⇒    $=(\frac{3.038}{0.3})^2$

⇒    $=102.5494 \sim 102$