Question

1. There is some concern that pollutants are negatively affecting frog sex ratio. (Amphibian sex is environmentally, not genetically, determined.) Previous research has shown a population will suffer negative effects if more than 60% of the animals are female. In order to determine if there are dangerously many female frogs in a population, biologists collected a sample of 37 frogs, and found that 26 of the frogs were female. Perform a hypothesis test, at a=0.05, to determine if more than 60% of the frogs in the population are female.
   1. State the null and alternative hypotheses.
   2. Find a test statistic and p-value.
   3. Make a decision. (At alpha = 0.05)
   4. Interpret the results of c and d in context.

Could you show/ explain your work? I would like to understand how to solve this problem. Thank you!

Answer 1

Solution :

This is the right tailed test .

a) The null and alternative hypothesis is

H₀ : p = 0.60

H_a : p > 0.60

= x / n = 26/37 = 0.7027

P₀ = 0.60

1 - P₀ = 1-0.60 = 0.40

b) Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.7027 - 0.60/ [0.60*(0.40) /37 ]

= 1.275

P(z > 1.275) = 1 - P(z < 1.275 ) = 0.1011

P-value = 0.1011

c) = 0.05    

p=0.1011 ≥ 0.05

Fail to reject the null hypothesis .

d) There is there is not enough evidence to claim that the population proportion p is greater than p₀​, at the α=0.05 significance level.