Question

Please answer True or False for the following statements:

1.) In hypothesis testing, if the null hypothesis is rejected, then the alternative or motivated hypothesis must also be rejected.

2.) Under certain conditions, binomial distributions can be approximated by normal distributions.

3.) Using a normal distribution to approximate binomial probabilities is extremely accurate, but takes an excessive amount of time and should be avoided.

4.) A bell-shaped curve is still normal, even if the mean, median, and mode are not the same.

5.) Under a one-tailed test with the level of significance set at .05, the probability of erroneously rejecting a true hypothesis is .05.

Answer 1

(1) False

> If the null hypothesis is rejected, it favours in the support of alternative hypothesis. So, the alternative hypothesis is accepted.

(2) True

> The condition is that the sample size (n) must be sufficiently large such that np>10 and n(1-p)>10.

(3) False

> The normal distribution to approximate binomial distribution is not accurate, but it is easy to use and doesn't take too much time.

(4) False

> For normal distribution mean, median and mode are same.

(5) True

> Type I error is the rejecting a true null hypothesis. And the probability of type I error is equal to the significance level. So the probability of erroneously rejecting a true hypothesis is 0.05.