15 Feeding fish In the midwestern United States a large aqua

15. Feeding fish In the midwestern United States, a large aquaculture industry raises largemouth bass. Researchers wanted to know whether the fish would grow better if fed a natural diet of fathead minnows or an artificial diet of food pellets. They stocked six ponds with bass fingerlings weighing about 8 grams. For one year, the fish in three of the ponds were fed qiinnov.is, and the others were fed the commercially prepared pellets. The fish were then harvested, weighed, and measured. The bass fed a natural food source had a higher average length (19.6 cm) and weight (95.9 g) than those fed the commercial fish food (17.3 cm and 72.0 g. respectively). The researchers reported P-values for both measurements to he less than 0.001. a) Explain to someone who has not studied Statistics what the P-values mean here. b) What advice should the researchers give the people who raise largemouth bass? c) If that advice turns out to be incorrect, what type of error occurred?

Solution

p value:

For performing any hypothesis test to check the claim for statistical proof, a percent level is set. The percent is called significant level. Normally it is called alpha and will be a small value as 0.1, 0.05 or 0.01.

Lower alpha values may give more accurate result.

The  the p-value is a function of the observed sample results (a statistic) that is used for testing a statistical hypothesis.

Based on the data and our assumption the prob for test statistic is obtained using z distribution or t distribution.

If the p-value is equal to or smaller than the significance level (?), it suggests that the observed data are inconsistent with the assumption that the null hypothesis is true, and thus that hypothesis must be rejected and the alternative hypothesis is accepted as true. When the p-value is calculated correctly, such a test is guaranteed to control the Type I error rate to be no greater than ?.

The p-value is calculated as the lowest ? for which we can still reject the null hypothesis for a given set of observations. An equivalent interpretation is that p-value is the probability of finding the observed sample results, or \"more extreme\" results, when the null hypothesis is actually true (where \"more extreme\" is dependent on the way the hypothesis is tested).

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As p value <0.001, reject null hypothesis. There is a significant increase of growth if fed minnows or natural diet compared to others.

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If advice turns to be incorrect, we rejected a true null hypothesis. i.e. type I error has occurred.