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# Statistics: Caffeine consumption of a sample of 49 adult women

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A summary on the daily consumption of caffeine for a sample size of 49 adult women produced:

Ð? = 49
X bar = 215 mg
s = 235 mg
range: 5 to 1176

1. Does it appear plausible that the population distribution of daily caffeine consumption is normal? Explain

2. Is it necessary to assume a normal population distribution to estimate the value of the population mean consumption µ? Explain

3. Suppose it had previously been believed that mean consumption µ was at most 180 mg. Does the given data contridict this prior belief? Explain.

#### Solution Preview

A summary on the daily consumption of caffeine for a sample size of 49 adult women produced:

n = 49
X bar = 215 mg
s = 235 mg
range: 5 to 1176

1. Does it appear plausible that the population distribution of daily caffeine consumption is normal? Explain

It does not appear that the distribution of caffeine consumption is normal. Notice that the mean of 215 is less than 1 standard deviation above 0, the smallest possible value of caffeine consumption. There are therefore no observations in the data that are less than 1 standard deviation below the mean. Notice also that the largest observation in the data is 1176. The z-score for this value is:

For normally distributed data, we expect almost all the data to be within 3 ...

#### Solution Summary

The expert statistical analyzes caffeine consumption of a sample of 49 adult women.

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