Hypothesis testing, confusion between null and alternative hypothesis?

Question

I only need to know what do you think the null and altenative hypothesis is!

The story:
A plant breeder claims that a new variety of fruit bush he has produced gives a higher yield of fruit than the variety it will replace. A random sample of 10 bushes of the new variety is grown and the yields of the bushes recorded. The old variety has an average yeild of 5.2kg/bush. It is assummed that the yield from each bush is an independent observation from a normal distribution. Test at 5% level of significance, the breeder's claim.

I felt that
(null hypothesis) H0: mean=5.2
(alternative hypothesis) H1: mean<5.2

but my teacher said that it shoulde be:
(null hypothesis) H0: mean=5.2
(alternative hypothesis) H1: mean>5.2

Side question: How big is the range of the p-value(observed significance value)?

so what is the null or alternative hypothesis for the story?

Answer 1

Your teacher is right.

Think of the null hypothesis as the status quo, that nothing has changed. (That is why it is called the null hypothesis: null is a fancy word for nothing, in statistical testing, no deviation or change from the nominal value.) In a trial, the null hypothesis might be likened to the defense and is presumed innocent of being false until proven guilty beyond a reasonable doubt.

The alternative hypothesis is the challenger, the one who has the burden of proof, the one making the claim that something has changed, that things are not as they have always been. The alternative hypothesis would be likened to the prosecution or the accuser in a trial. In a statistical test of this kind, the alternative hypothesis never includes equality to the nominal value.

Whether the test is two-tailed or one-tailed depends on the alternative hypothesis, whether the advocate can make its case that the null hypothesis is substantially false regardless of which way the data is off nominal. As an example of a one-tailed test, consider the consumer advocate who is claiming that the failure rate of a product is greater than the manufacturer's claim. Clearly, the consumer advocate will have trouble persuading anyone to take corrective action against a manufacturer whose product's failure rate is substantially lower than promised.

The level of significance is the reasonable doubt, the risk that the court is willing to take of wrongly convicting the null hypothesis of being false even if the statistic under test is in fact at nominal value.

The trial itself consists of the statistical sampling and subsequent analysis of the results.

Sometimes, the problem is so sketchily or poorly worded that it is unclear which contender is advocating the alternative hypothesis, but not in this case. There is presumably a fair amount of data already on the yield of the old variety and it can be reasonably inferred that the old variety has been in production for a while. This is the baseline, the status quo, that the new variety must improve upon to justify removing the old bushes and replacing them with the new variety. The burden of proof is therefore on the plant breeder's claim that the new variety is better than the old. Furthermore, the breeder isn't merely claiming that the new variety is as good as the old, which would include equality, but better. The breeder's claim is therefore the alternative hypothesis both because the breeder is the challenger and is making a claim that results at nominal value would falsify.

The p-value is the probability of getting a result at least as unfavorable to the null hypothesis as was actually gotten, assuming that the population statistic being tested is actually at its nominal value. The p-value may therefore be considered to be the actual risk of rejecting the null hypothesis. This is compared against the level of significance, which is the risk that the court (parties interested in the results of the test) have agreed upon for wrongly rejecting the null hypothesis. If the p-value is less than the level of significance, the risk of wrongly rejecting the null hypothesis is deemed acceptably low. The null hypothesis would therefore be rejected and the alternative hypothesis presumed true.

In this example, the risk was set at 5%, or a probability of 0.05. This particular test cannot be conducted because there is not yet any data from which the sample mean and standard error of the mean can be deduced, hence nothing from which to compute a p-value.

Answer 2

The null alternative is the two varieties are the same So the mean would be at 5% level the mean is 5.2

The alternative hypothesis would be that the mean are different so mean<5.2 or mean>5.2 would be alternative.

But no you must think , that the breeder is not unterested by the bad result so in the problem you take in account only the second hypothesis

Answer 3

An alternative would be another proposed explanation. It requires evidence the same as the original hypothesis. The null hypothesis is just the default position as it says you don't believe the hypothesis because there is no evidence. Since it is the default it only requires evidence to counter other other evidence.

Answer 4

your teacher is right. He wants to know if the new variety givess a higher yield of fruit. That is, mean > 5.2
A plant breeder claims that a new variety of fruit bush he has produced gives a higher yield of fruit than the variety it will replace.

Answer 5

Hypothesis is some assumed situation.