Q1. John Kleman is the host of the KXYX Radio AM drive-time news in Denver. Duri

Question

Q1. John Kleman is the host of the KXYX Radio AM drive-time news in Denver. During his morning program, John asked listeners to call in and discuss current local and national news. This morning, john was concerned with the numbers of hours children under 12 years of age watched TV per day. The last 5 callers reported that their children watched the following numbers of hours of hours of TV last night.
3.0, 3.5, 4.0, 4.5, 3.0
Would it be reasonable to develop a confidence interval from these data to show the mean number of hours of TV watched? If yes, construct an
appropriate confidence interval and interpret the result. If no, why would a confidence interval not be appropriate?

Explanation / Answer

No, it be reasonable to develop a confidence interval from these data to show the mean number of hours of TV watched.The confidence interval would not be appropriate becuase of the following reasons:-

1. The sample size is very small (only 5 values). Smaller sample sizes generate wider intervals. There is an inverse square root relationship between confidence intervals and sample sizes. If you want to cut your margin of error in half, you need to approximately quadruple your sample size. Hence, for a small sample size the margin of error will be very high.

2. The sample may not be random. For such a small sample size , it may happen that the sample might be chosen non - randomly. The confidence intervals are computed on the assumption of a simple random sample, that the data is collected from a representative, randomly selected portion of the total population.

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