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Molodets [167]
3 years ago
15

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.
Mathematics
1 answer:
ratelena [41]3 years ago
3 0

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

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