Question

A 90% confidence interval for a population mean is given as (17.68, 22.02). This confidence interval is based on a simple random sample of 36 observations. Calculate the sample mean and standard deviation. Use the t-distribution in any calculations.

Answer 1

Answer:

The correct solution is "7.704". The further explanation is given below.

Step-by-step explanation:

According to the question,

$t_{\alpha/2},df = 1.690$

Sample mean,

$\bar{x} = \frac{(17.68 + 22.02)}{2}$

  $=19.85$

The Margin of error (E),

= $Upper \ confidence \ interval - \bar{x}$

= $22.02 - 19.85$

= $2.17$

Now,

⇒ $s = \frac{ E\times \sqrt n }{t_{\alpha/2},df}$

      $=\frac{ 2.17\times \sqrt 36 }{ 1.690}$

      $= 7.704$