A study from 2014 found that adults in the US spend an average of 11 hours per day watching, reading, listening to or simply interacting with media. Researchers at UCLA suspect students spend less time engaging media. They grouped UCLA students by class section, randomly selected 20 class sections, and administered a survey to each student in those randomly selected class sections. The following data represents the mean time (in hours) per day spent engaging media for each of the randomly selected classes:9.511.56.07.589.510.511128.259.58.29.310.811138.69.510.5What would be the 99% Confidence Interval for mean time (in hours) spent per day engaging media for UCLA students. Do this "by hand", using appripriate symbols/formulas/tables.

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Asked Apr 30, 2019
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A study from 2014 found that adults in the US spend an average of 11 hours per day watching, reading, listening to or simply interacting with media. Researchers at UCLA suspect students spend less time engaging media. They grouped UCLA students by class section, randomly selected 20 class sections, and administered a survey to each student in those randomly selected class sections. The following data represents the mean time (in hours) per day spent engaging media for each of the randomly selected classes:

9.5 11.5 6.0 7.5 8 9.5 10.5 11 12 8.2
5 9.5 8.2 9.3 10.8 11 13 8.6 9.5 10.5

What would be the 99% Confidence Interval for mean time (in hours) spent per day engaging media for UCLA students. Do this "by hand", using appripriate symbols/formulas/tables. 

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Expert Answer

Step 1

Find the distribution that has to be used to construct the confidence interval in the given situation:

It is given that, a sample of size 20 class sections is used to estimate the population mean time spent per day in engaging media by UCLA students.

The sample size is n = 20.

Assume that the population of class sections of UCLA students is normally distributed.

The required conditions for using t distribution to estimate the confidence interval about mean is given below:

  • The population standard deviation σ must be unknown.
  • Either the sample size (n) must be greater than 30 or the population must be normally distributed.

Here, the population standard deviation is unknown.

The population from which the sample is drawn is assumed to be normally distributed.

Thus, the t–distribution is used to construct the confidence interval for the population mean in the given situation.

The approximate 100*(1–α)% confidence interval for the population mean will be obtained using the formula given below:

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Step 2

Find the sample mean and standard deviation for the mean times of 20 class sections:

Excel procedure to find the mean and standard deviation for sample of 20 sections:

Step 1: Enter the values of mean times spend in engaging media for 20 sections from A2:A21.

Step 2: Obtain the sample mean in cell B22, by entering the formula “=AVERAGE(A2:A21)”.

Step3: Obtain the sample standard deviation in cell B23, by entering the formula “=STDEVA(A2:A21)”.

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Step 3

Obtain the critical value:

The required confidence level is 100*(1–α)% = 99%.

The critical value...

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