Use the table to determine whether mean alc content of all wines for that grape in 2012 in Italy was greater than 12.75% at the 0.1 significance. a) State the null and alternaternative hypothesis. b) What is the calculated value of the associated test statistic and what is the critical value of the associated test statistic? c) State your decision about the null hypothesis by comparing calculated and critical values of the statistic. State your conclusion(describe what the decision means in this problem).
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
A wine enthusiast named Suds collected data on the alc content (percent by volume) of wine for one grape variety in 2012 by a random sample of winemakers in Italy. Suds created the following Table:
| Alcohol % | |
| 13.093 | |
| Std Error | 0.1143 |
| 13.165 | |
| 13.17 | |
| Std Deviation | 0.5111 |
| Sample Variance | 0.2612 |
| Kurtosis | -0.8385 |
| Skew | -0.1747 |
| 1.68 | |
| Minimum | 12.2 |
| Maximum | 13.88 |
| Sum | 261.86 |
| Count | 20 |
Use the table to determine whether mean alc content of all wines for that grape in 2012 in Italy was greater than 12.75% at the 0.1 significance.
a) State the null and alternaternative hypothesis.
b) What is the calculated value of the associated test statistic and what is the critical value of the associated test statistic?
c) State your decision about the null hypothesis by comparing calculated and critical values of the statistic. State your conclusion(describe what the decision means in this problem).
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