A market surveyor wishes to know how many energy drinks teenagers drink each week. They want to construct a 85% confidence interval for the mean and are assuming that the population standard deviation for the number of energy drinks consumed each week is 1.2. The study found that for a sample of 830 teenagers the mean number of energy drinks consumed per week is 7.3. Construct the desired confidence interval. Round your answers to one decimal place.

So on this case the 85% confidence interval would be given by (7.2;7.4)  

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

represent the sample mean

population mean (variable of interest)

represent the population standard deviation

n=830 represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

  (1)

Since the Confidence is 0.85 or 85%, the value of and , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.075,0,1)".And we see that

Now we have everything in order to replace into formula (1):

So on this case the 85% confidence interval would be given by (7.2;7.4)    

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step-by-step explanation:

step-by-step explanation: