Question

Metal Tags on Penguins and Breeding Success

A study was designed to test whether applying metal tags is detrimental to a penguin. The scientists studied the breeding success of the metal and electronic tagged penguins. Metal tagged penguins successfully produced offspring in 32% of the 122 total breeding seasons, while the electronic tagged penguins succeeded in 44% of the 160 total breeding seasons.

Construct a 95% confidence interval for the difference in proportion successfully producing offspring (pM-pE). Let pM be the proportion of penguins with metal tags that succeeded in breeding and pE be the proportion of penguins with electronic tags that succeeded in breeding.

Round your answers to three decimal places.

The 95% confidence interval is _________________ to ________________

Answer 1

For Metal tagged penguins:

n1 = 122, p̂1 = 0.32

For electronic tagged penguins:

n2 = 160, p̂2 = 0.44

95% Confidence interval for the difference:  

At α = 0.05, two tailed critical value, z_c = NORM.S.INV(0.05/2) = 1.960

Lower Bound = (p̂1 - p̂2) - z_c*√ [(p̂1*(1-p̂1)/n1)+(p̂2*(1-p̂2)/n2) ]

= (0.32 - 0.44) - 1.96*√[(0.32*0.68/122) + (0.44*0.56/160)] = -0.2330

Upper Bound = (p̂1 - p̂2) + z_c*√ [(p̂1*(1-p̂1)/n1)+(p̂2*(1-p̂2)/n2) ]

= (0.32 - 0.44) + 1.96*√[(0.32*0.68/122) + (0.44*0.56/160)] = -0.0070

-0.233 < p_M -p_E < -0.007