Ants are capable of chemically discriminating between nestmates and non-nestmates. Ozaki et al. (2005) discovered sensory cells in the antennae of ants that respond only to the cuticular hydrocarbons (CHCs) of non-nestmates. They showed that 42 of 48 head-attached antenna preparations responded to chemical extracts of CHC compounds obtained from non-nestmates. Use likelihood to estimate the proportion of preparations p responding to non-nestmate CHC extracts.

a. Using a computer program, calculate the log-likelihood of a series of values of p between 0.50 and 0.99 in increments of 0.01. Draw the relationship between the loglikelihood and p with a log-likelihood curve.

b. Find the maximum likelihood estimate for p to two decimal places.

c. Calculate the likelihood-based 95% confidence interval for the parameter p.