CSIR NET Mathematics 2024|Testing of Hypothesis |17 April 2024

Let P be the probability that a coin will fall head in a single toss in order to test  against . The coin is tossed 5 times and H₀ is rejected if more than 3 heads are obtained. Find the probability of power of the test?

To test  vs

a random sample of size 5 is taken from the process if the number of defectives is 4 or more, the null hypothesis is rejected what is the probability of rejecting

H₀ if ?

Let x have a binomial distribution with parameter n and P, n = 3. For testing the hypothesis  vs against . Let a test be “reject H₀ if and accept H₀ if ”. The probability of type – I and type –II errors respectively are

Let x be a random sample of size distribution. For testing  against  the critical region  has to find P{type-II error if } = ?

What is the corresponding p-value?