Question

Food under refrigeration must be stored at 40° F or below to prevent the growth of bacteria and spoilage. A commercial refrigerator’s temperature will vary according to a normal distribution with a standard deviation σ = 0.5°. A 90% confidence interval for the mean temperature, using a random sample of four commercial refrigerators, is (39.032, 39.768)

The margin of error in this confidence interval is ± degrees 3 points

Due to the presence of arsenic in ground water, some apple juices contain amounts of arsenic that could have detrimental health effects for small children. Researchers at the FDA tested 94 apple juice samples for arsenic, and reported a 95% confidence interval for the mean arsenic content is 5.33 ppb to 7.27 ppb.

The margin of error in this confidence interval is ± ppb.

Answer 1

Solution :

Given that,

Lower confidence interval = 39.032

Upper confidence interval = 39.768

  = (Lower confidence interval + Upper confidence interval ) / 2

= (39.032 + 39.768) / 2

= 78.8 / 2 = 39.4

= 39.4

Margin of error = E = Upper confidence interval -   = 39.768 - 39.4 = 0.368

Margin of error = 0.368

The margin of error in this confidence interval is ±368

Lower confidence interval = 5.33

Upper confidence interval = 7.27

  = (Lower confidence interval + Upper confidence interval ) / 2

= (5.33 + 7.27) / 2

= 12.6 / 2 = 6.3

= 6.3

Margin of error = E = Upper confidence interval -   = 7.27 - 6.3 = 0.97

Margin of error = 0.97

The margin of error in this confidence interval is ± 0.97