The side length of aDavid is a statistician. He has a sample size of 40 (which he cannot change). What element of his hypothesis test can he adjust to minimize the probability that he incorrectly rejects the null hypothesis?
the mean of the population
the mean of the sample
the standard deviation of the population
the significance level of the testn equilateral triangle is 6 cm. What is the height of the triangle?

Answers

Answer 1

Answer: D) the significance level of the test

=======================================================

Explanation:

The significance level of the test, also known as "alpha", is the probability of making a type 1 error. A type 1 error is where you reject the null hypothesis but it was true all along.

The null hypothesis is where we test a certain probability distribution (eg: normal distribution). Specifically we gather a sample of values and compute the test statistic. If the probability of getting that test statistic or more extreme is smaller than alpha, then we reject the null. This probability value is known as the p-value.

If you lower the alpha value, then that will make it more likely you do not reject the null. Consider an example where alpha = 0.10 to start with. If you get a p-value of 0.02, then you would reject the null. The same would apply for alpha = 0.05; however, with alpha = 0.01, the p-value is no longer smaller than alpha. At this point we do not reject the null. Your textbook may use the phrasing "fail to reject the null".

Going in the opposite direction, increasing the alpha value will make it more likely to reject the null. Each time you adjust the alpha value, keep the p-value to some fixed number (between 0 and 1).

Answer 2

The height of the equilateral triangle is 3√3 cm.

What is hypothesis testing?

Hypothesis testing is a statistical method that is used to make decisions about a population based on a sample of data.

It involves testing a null hypothesis (H0) against an alternative hypothesis (Ha) using statistical techniques.

We have,

To minimize the probability of incorrectly rejecting the null hypothesis in a hypothesis test with a fixed sample size of 40, the statistician can adjust the significance level of the test.

The significance level, denoted by α, is the probability of rejecting the null hypothesis when it is actually true.

By choosing a smaller significance level, the statistician can decrease the probability of making a Type I error (rejecting the null hypothesis when it is actually true).

However, decreasing the significance level also increases the probability of making a Type II error (failing to reject the null hypothesis when it is actually false).

Therefore,

The choice of significance level involves a trade-off between the two types of errors and should be based on the specific context of the problem and the consequences of each type of error.

Now,

The height of an equilateral triangle can be found using the formula:

height = (side length / 2) x √3

The side length = 6 cm

So,

height = (6 / 2) x √3

           = 3√3 cm

Therefore,

The height of the equilateral triangle is 3√3 cm.

Learn more about hypothesis testing here:

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Answers

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Answers

Step-by-step explanation:

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Answers

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Answers

Answer:

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Answers

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Learn more about slopes here:

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Answers

Answer:

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Answers

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