## Related questions with answers

The alcohol content of wine depends on the grape variety, the way in which the wine is produced from the grapes, the weather, and other influences. Here are data on the percent of alcohol in wine produced from the same grape variety in the same year by 48 winemakers in the same region of Italy:

12.86 12.88 12.81 12.70 12.51 12.60 12.25 12.53 13.49 12.84

12.93 13.36 13.52 13.62 12.25 13.16 13.88 12.87 13.32 13.08

13.50 12.79 13.11 13.23 12.58 13.17 13.84 12.45 14.34 13.48

12.36 13.69 12.85 12.96 13.78 13.73 13.45 12.82 13.58 13.40

12.20 12.77 14.16 13.71 13.40 13.27 13.17 14.13

(a) Make a histogram of the data, using class width 0.25. The shape of the distribution is a bit irregular, but there are no outliers or strong skewness. There is no reason to avoid use oft procedures for n = 48.

(b) Give a 95% confidence interval for the mean alcohol content of wine of this type. (c) Based on your confidence interval, is the mean alcohol content significantly different at the a = 0.05 level from 12%? From 13%?

Solution

Verified(a) Create a histogram. The width of the bars has to be the same and the height has to be equal to the frequency.

Shape: Roughly symmetric/bell-shaped and thus the distribution is roughly normal.

Center: $\overline{x}=13.1538$

Spread: $s=0.5302$

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