The inspection division of the lee county weights and...

The inspection division of the Lee County Weights and Measures Department is interested in estimating the actual amount of soft drink that is placed in two liter bottles at the local bottling plant of a large nationally known soft-drink company. The bottling plant has informed the inspection division that the population standard deviation for two liter bottles is known to be 0.05 liters. A random sample of 60 two liter bottles obtained from this bottling plant indicates a sample average of 1.98 liters. (a) Construct a 95% confidence interval for the population mean amount of soda in a two liter bottle and interpret it. (b) Is there evidence that the factory is under filling the bottles? Justify

Transcript

00:01 So what is the statistics problem? but before i get started, i recommend me to the questionnaire self and come back to see if we got a right now.

00:08 So hopefully you've done the questionnaire yourself.

00:10 Now let's work together.

00:11 So we're given the inspection division.

00:13 A department is interested in estimating the actual amount of soft drink in a 2 liter bottle.

00:19 The borrowing plant has informed that the inspection unit population.

00:23 So we're given a bunch of numbers.

00:25 And what we want to know is construct 95 % confidence interval for but the population mean amount of soda, into a little bottle, interpret it.

00:35 And then is there an evidence that the factory is underflowing the bottle? so basically testing the normal hypothesis.

00:43 So what i think would be helpful is writing down the data that we're given so that it becomes easier to calculate if you have all the data displayed in front of us.

00:50 So we're given that sigma is 0 .05 in the question.

00:54 We're given the sample number, which is 60, and the.

00:58 We're given 1 .m.

01:01 Average, 1 .98 liters.

01:06 Okay, meters.

01:10 And then we want to construct a 95 % confidence interval.

01:14 The appropriate formula for this is f plus minus z sigma over root n.

01:26 And then if we go to our table, statistical tables, if you go to table you have the next year table three if you go to three you will find that the z star is equal to 1 .96 when there is a 95 % confidence interval so we can do our data here on 1 .598 plus minus 1 .96 0 .0 .0505 over 60 so so 1 .99 plus minor calculator about 0 .0 ,0, 127.

02:05 And if you actually do the numbers, you should get the interval...

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