Question

A study of 16 randomly selected people had 5 of them say that they believe in extra-terrestrial life, 10 say they did not, and 1 person declined to answer. Use the sign test at the 0.05 significance level to test the claim that the minority of people believe in extra-terrestrial life.

(a) What is the value of the test statistic used in this sign test?



(b) What is the critical value in this sign test?



(c) What is the correct conclusion of this sign test?

• There is sufficient evidence to support the claim that the minority of people believe in extra-terrestrial life.
• There is not sufficient evidence to support the claim that the minority of people believe in extra-terrestrial life.
• There is not sufficient evidence to warrant rejection of the claim that the minority of people believe in extra-terrestrial life.
• There is sufficient evidence to warrant rejection of the claim that the minority of people believe in extra-terrestrial life.

Answer 1

1.Here

The number of positive signs = 5

The number of negative signs = 10

The one declined to answer = The number of values is zero= 1.

Clearly, we can ignore the last one.

Now, here we need to check whether the minority believed that the extra terrestrial life exist or not. Therefore the hypothesis will be

The value of test statistic = ==.

B) We know that,

.

Using the significance level , we can see that,

Now when the probability greater than level of significance hence the critical region is obtained as

C). The number of positive signs = 5. Therefore it lies in the acceptance region.

Therefore, the answer is :

There is not sufficient evidence to support the claim that the minority of people believe in extra-terrestrial life.