Question

There were 324 adults surveyed. Among the participants, the mean number of hours of sleep each night was 7.5 and the standard deviation was 1.6. The margin of error, assuming a 95% confidence level, is approximately . Round to the nearest hundredth

Answer 1

0.17 sense you have to round it to the nearest hundreth

Answer 2

Answer with explanation:

Total Population Being Surveyed = 324

Mean of the Population = 7.5

Standard Deviation =1.6

Margin of Error is given by the formula

    $=Z_{\text{value at 95 percent confidence interval}}\times \frac{\text{Standard deviation}}{\sqrt{\text{Sample size}}}\\\\=1.96 \times \frac{1.6}{\sqrt{324}}\\\\=1.96\times \frac{1.6}{18}\\\\=\frac{3.136}{18}\\\\=0.1742$

Marginal of Error = 0.17 (approx)  

Mean =7.5

Confidence Interval for a population when Z score at 95% is calculated  =Mean $\pm$ margin of error

    =that is between ,7.50 +0.17 to ,7.50 -0.17

  =Between ,7.33 to 7.67