Binomial Distribution: Find Critical Values

Examples, solutions, videos, activities, and worksheets that are suitable for A Level Maths. In this lesson, we will learn Hypothesis Testing for a Binomial Distribution.

Hypothesis Testing - Critical Values - Two Tail Test - Binomial Distribution
In this example you are shown how to find the upper and lower critical values and the actual significance of a test.
Example:
A person suggests that the proportion, p of red cars on a road is 0.3. In a random sample of 15 cars it is desired to test the null hypothesis p = 0.3 against the alternative hypothesis p ≠ 3 at a nominal significance level of 10%. Determine the appropriate rejection region and the actual significance level.

Statistics: Hypothesis testing critical value method for a Binomial Distribution example
Quite often we can find the critical value for a given test and also this can be used an alternative method of testing a hypothesis.
One tail tests for a binomial distribution.
Example:
A manufacturer claims that 2 out of 5 people prefer soapy suds washing powder over any other brand. For a sample of 25 people, only 4 people are found to prefer Soapy Suds. Is the manufacturer’s claim justified? Test at the 5% level of significance.

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Hypothesis testing - Finding an Upper Critical Value for the Binomial Distribution
In this example you are required to work out the upper critical value for a Binomial Distribution. Example:
A particular drug has a 1 in 4 chance of curing a certain disease. A new drug is developed to cure the disease. How many people would need to be cured in a sample of 20 if the new drug was to be deemed more successful at curing the disease than the old drug to obtain a significant result at the 5% level?

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