Question

Weight Loss in Men Many polls have asked people whether they are trying to lose weight. A Gallup poll in November 2008 showed that 22% of men said they were seriously trying to lose weight. In 2006, 24% of men (with the same average weight of 194 pounds as the men polled in 2008) said they were seriously trying to lose weight. Assume that both samples contained 500 men.

1. Determine whether the difference in proportions is significant at the 0.05 level.

2. Repeat the problem with the same proportions but a sample size of 5000 instead of

   500.

3. Comment on the different p-values and conclusions with different sample sizes.

Answer 1

A)

n1= 500, n2 = 500, =0.05

= 22% = 0.22,  

= 24% = 0.24

Ho: P1 = P2

Ha: P1 P2

Z = -0.751

Test Statistics = -0.75

P-Value = 2* P(Z < -0.75)

P(Z < -0.75) = 0.2266

P-Value = 2* 0.2266

P-Value = 0.4532

since, (P-Value = 0.4532) > ( =0.05)

Hence Failed to reject Ho

Therefore there is not significant difference between two proportions.

B)

n1= 5000, n2 = 5000, =0.05

= 22% = 0.22,  

= 24% = 0.24

Ho: P1 = P2

Ha: P1 P2

Z = -2.376

Test Statistics = -2.38

P-Value = 2* P(Z < -2.38)

P(Z < -2.38) = 0.0087

P-Value = 2* 0.0087

P-Value = 0.0174

since, (P-Value = 0.0174) < ( =0.05)

Hence Reject Ho

Therefore there is a significant difference between two proportions.

C)

When Sample size (n) = 500 then P-Value = 0.4532

Therefore there is not significant difference between two proportions.

When Sample size (n) = 5000 then P-Value = 0.0174

Therefore there is a significant difference between two proportions.