Question

Proportion data follow the binomial distribution, which can be approximated by the normal distribution if np>=5 and nq>=5

True or False?

The sample Proportion p̄=x/n where x is the number of successes and n is the sample size

True or false?

The Type-II error β is the probability of failing to reject a true null Hypothesis Ho.

True or false?

The only way to lower the probability of both errors α and β at the same time, is to decrease the sample size.

True or false?

In Binomial Distribution, If p=40% then the probability of successes is 60%

True or False?

Answer 1

1)

Proportion data follow the binomial distribution, which can be approximated by the normal distribution if np>=5 and nq>=5

True

2)

The sample Proportion p̄=x/n where x is the number of successes and n is the sample size.

True

3)

The Type-II error β is the probability of failing to reject a true null Hypothesis Ho.

False.

Type II error is failing to reject H0 when it is false.

4)  

The only way to lower the probability of both errors α and β at the same time is to decrease the sample size.

False

The probability of a type 1 error (rejecting a true null hypothesis) can be minimized by picking a smaller level of significance α before doing a test (requiring a smaller p-value for rejecting H0).

Once the level of significance is set, the probability of a type 2 error (failing to reject a false null hypothesis) can be minimized either by picking a larger sample size or by choosing a "threshold" alternative value of the parameter in question that is further from the null value.

5)

In Binomial Distribution, If p=40% then the probability of successes is 60%

False.

P= 0.40 then probability of success is 40 %