Question

2. Let X have a binomial distribution with the number of trials $n = 10$ and with $p$ either $1/4$ or $1/2$. The simple hypothesis $H_0: p = 1/2$ is rejected, and the alternative simple hypothesis $H_1: p = 1/4$ is accepted, if the observed value of $X_1$, a random sample of size 1, is less than or equal to 3. (a) Should we consider it as a large sample test or small sample test? (b) Find the significance level and the power of the test.

          2. Let X have a binomial distribution with the number of trials $n = 10$ and with $p$ either $1/4$ or
$1/2$. The simple hypothesis $H_0: p = 1/2$ is rejected, and the alternative simple hypothesis
$H_1: p = 1/4$ is accepted, if the observed value of $X_1$, a random sample of size 1, is less than
or equal to 3.
(a) Should we consider it as a large sample test or small sample test?
(b) Find the significance level and the power of the test.

2. Let X have a binomial distribution with the number of trials n = 10 and with p either 1/4 or
1/2. The simple hypothesis H0: p = 1/2 is rejected, and the alternative simple hypothesis
H1: p = 1/4 is accepted, if the observed value of X1, a random sample of size 1, is less than
or equal to 3.
(a) Should we consider it as a large sample test or small sample test?
(b) Find the significance level and the power of the test.

Added by Darius W.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Lien Le

01/03/2024

Step 1

Therefore, it is a small sample test. Show more…

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2. Let X have a binomial distribution with the number of trials n = 10 and with p either 1/4 or 1/2. The simple hypothesis Ho: p = 1/2 is rejected, and the alternative simple hypothesis H₁: p = 1/4 is accepted, if the observed value of X1, a random sample of size 1, is less than or equal to 3. (a) Should we consider it as a large sample test or small sample test? (b) Find the significance level and the power of the test.