You wish to find a 95% confidence interval for the mean number of times men change channels with a remote control during a commercial. based on a preliminary study, you estimate σ = 15. how many commercials' worth of data do you need to have a margin of error no more than 3?

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Mathematics

Tiara Cameron

3 March, 12:51

You wish to find a 95% confidence interval for the mean number of times men change channels with a remote control during a commercial. based on a preliminary study, you estimate σ = 15. how many commercials' worth of data do you need to have a margin of error no more than 3?

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Gauge Cohen · Answer 1

For margin of error to be a maximum of 3:

3 = z * (SD / sqrt (n)), where z is the z-score, SD is the standard deviation and n is the sample size.

z = 1.96 for a 95% confidence interval, and we are given SD = 15.

3 = 1.96*15/sqrt (n)

sqrt (n) = 9.8

n = 96.04 ~ 96 commercials.