A quality control inspector selects 12 bottles of apple juice at random from a single day’s production. The mean amount of apple juice in the bottles is 298.3 milliliters, and the 95% confidence interval for the true mean amount of juice dispensed per bottle is (296.4, 300.2). Does this interval give the quality control inspector reason to believe that the mean amount of juice in today’s bottles differs from 300 milliliters, as the juice label promises?

The juice label (300ml) is in the confidence interval.

So, the 95% CI does not give the inspector the reason to believe the amount of juice differs from 300ml

Step-by-step explanation:

Given

From the 95% confidence interval value, we have: 296.4 to 300.2

Within this interval, we can find the juice label 300

i.e. 296.4 < 300 < 300.2

In other words, the juice label (300ml) is in the confidence interval.

So, the 95% CI does not give the inspector any reason to believe the amount of juice differs from 300ml.

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step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)

step-by-step explanation: