A political candidate wishes to determine if endorsing increased social spending is likely to affect her standing in the polls. She has access to data on the popularity of several other candidates who have endorsed increased spending. The data was available both before and after the candidates announced their positions on the issue. The data are as follows:

Candidate Popularity Ratings

BeforeAfter

1 42 43

2 41 45

3 50 56

4 52 54

4 58 65

6 32 29

7 39 46

8 42 48

9 48 47

10 47 53

11 43 45

Assuming no other factors were influencing the popularity ratings

(1)State the nondirectional alternative hypothesis.

(1) State the null hypothesis.

(2) Compute the sign test. That is list the number of plusses and minuses that you obtain.

(2)What is the probability of observing the results above just by chance?

(2) State your conclusions.

(1)What type of error might you be making based upon your conclusions.