Answer to Question #100085 in Statistics and Probability for Juliet Beglaryan

Question

Suppose a child psychologist say that the average time that working mothers spend talking to their children is 11 minutes per day. a= 0.01. 1) in this case what is the Type I and Type II error?
2)what is P(type I error)

Answer 1

Type 1 error is the rejection of true null hypothesis, also known as false positive and type II error is the non rejection of false null hypothesis.

1)

In this case,

Null hypothesis is Average time that working mothers spend talking to their children is 11 minutes per day.

Now, the type 1 error will occur if we reject the null hypothesis even if it is true.

And the type 2 error will occur when we will accept the null hypothesis even if it is false.

2) P(type 1 error) = probability of rejecting null hypothesis given it is true.

We can reject the null hypothesis only when the P- value for this test will be less than the significance level, i.e 0.01

So, the probability of type 1 error is equal to the significance level which in this case is $0.01$

P(type 1 error)$=0.01$