Attached find example 6.7 from BioStatistics by Van Belle. Can someone please work out the problem in detail including explanations and calculations of the ptilda values.
Please explain what ptilda is and how does one compute the p value using ptilda.
Please give a clear complete explanation of the solution in detail© BrainMass Inc. brainmass.com October 4, 2022, 12:30 am ad1c9bdddf
SOLUTION This solution is FREE courtesy of BrainMass!
Please see the attached files.
In this problem we want to test the null hypothesis against the alternative hypothesis , where denotes the proportion.
Suppose denotes sample proportion in a sample of size n
Then can be taken as the test statistic and the corresponding critical (or rejection) region is given by , where c denotes the critical value.
It is given that n = 10 and = 0.2, thus we have
The p -value of this test is given by when the null hypothesis is true.
Therefore the p - value is given by
when the null hypothesis is true.
We know, if is the sample proportion in a sample of size n take from a population having proportion , then follows binomial distribution with parameters n and .
We have n = 10. Hence, when the null hypothesis is true, Y follows binomial distribution with parameters n =10 and = 0.5
Therefore the p- value is given by
= 0.0010 + 0.0098 + 0.0439 + 0.0098 + 0.0010 = 0.1094
Note: The probability values can be taken either from binomial tables or can be calculated by using excel function as follows = BINOMDIST (K, 10, 0.5, 0)
Answers to the specific questions:
1. (ptilda) is used to denote the proportion of a sample taken to conduct the test.
2. The p-value of a test is defined as the probability of obtaining a test value as large as the observed value when the null hypothesis was really true. The calculation of p- value by using is given in the description.
3. If the p-value is less than the specified significance level we reject the null hypothesis.