Question

Americans spend an average of 6.8 hours a night dreaming with a standard deviation of 1.2 hours. The middle 50% of sample means would fall between and for samples of 16. Round your answers to 3 decimal places and put the smaller mean before the larger mean.

Answer 1

The middle 50% of sample means for samples of 16, based on the given average and standard deviation, are approximately 6.212 to 7.388 hours.

Step-by-step explanation:

To find the middle 50% of sample means for samples of 16, we need to calculate the margin of error. The margin of error is equal to 1.96 times the standard deviation of the sample means, divided by the square root of the sample size. For a sample size of 16, the standard deviation of the sample means is 1.2 divided by the square root of 16, which is 0.3. Multiplying this by 1.96 gives a margin of error of 0.588. To find the range of sample means, we subtract the margin of error from the mean and add it to the mean. In this case, the range of sample means is 6.8 - 0.588 to 6.8 + 0.588, which is approximately 6.212 to 7.388.