Question

ch 20 nine randomly sampled students were asked how many hours of tv they watched last week. $\overline{x}=3.5$ h and $s = 4$ h. for 95% confidence and 8 degrees of freedom, $t^{*}=2.3$. the stemplot was roughly symmetrical, with no outliers. what is the 95% confidence interval for $m$?
$3.5\pm(2.3\times4/3)$
$3.5\pm(2.3\times4\times9)$
$3.5\pm(2.3\times4/9)$
$3.5\pm(2.3\times4)$

Explanation:

Step1: Recall the formula for confidence interval

The formula for a confidence interval for the population mean \( \mu \) when the population standard deviation \( \sigma \) is unknown is \( \bar{x}\pm t^{*}\frac{s}{\sqrt{n}} \), where \( \bar{x} \) is the sample mean, \( t^{*} \) is the critical value, \( s \) is the sample standard deviation, and \( n \) is the sample size.

Step2: Identify the values

Given \( \bar{x} = 3.5\), \( t^{*}=2.3\), \( s = 4\), and \( n = 9\). Then \( \sqrt{n}=\sqrt{9}=3\).

Step3: Substitute into the formula

Substitute the values into the formula \( \bar{x}\pm t^{*}\frac{s}{\sqrt{n}} \), we get \( 3.5\pm(2.3\times\frac{4}{3})\).

Answer:

\( 3.5\pm(2.3\times\frac{4}{3}) \) (the first option)