1. [5 marks] Inheritance relates to how a child receives genetic information from their parents. A scientist in the mid 19th century, Gregor Mendel, formulated "laws\" to understand genetic inheritance, known as Mendel 's laws of inheritance. (a) These laws infer that offspring in a second-generation cross have a 75% chance of carrying a dominant trait and a 25% chance of carrying a recessive trait. Inheritance occurs indepen- dently in each individual. What is the sampling distribution of the proportion of dominant traits in a second-generation cross yielding 711 individuals? [3] (b) A random sample of size n = 39 is obtained from a Normally-distributed population. A researcher will use the sample to test a hypothesis about the population mean. Is the Central Limit Theorem relevant to the conditions for this hypothesis test? Justify your answer. [2] 2. [12 marks] How many people use the internet to obtain health information? In a survey of 1790 randomly- selected adult Australian internet users, 1553 said that they obtain such information using the intemet. (a) Use these results to evaluate the evidence that at least 85% of adult Australian internet users get health information from the internet. Assume a = 1%, use a P-value approach, and include all relevant steps of a formal hypothesis test. [10] (b) Can the conclusion from part (a) be generalised to all of the Australian adult population? Explain why or why not. [2] 3. [7 marks] A recently opened bottle of wine will smell "off\" if sulphur compounds are sufficiently con- centrated. It is of interest to winemakers to determine the \"odour threshold\4. [16 marks] An experiment was conducted to investigate the effect of an electric eld on wound healing rates in newts (most animals have a weak electric eld). Thirty-three (33) newts were randomly allocated between a 'treatment' group and a 'control' group, and on each newt (in both groups) one hind limb was randomly designated the 'treatment' limb. In the treatment group, an electrode was applied to the treatment limb so that the electric field on that limb was changed to 1.5 times its natural value. The other hind limb was not treated. In the control group, no eld was applied. Identical incisions were made in both hind limbs of all the newts, and the healing rates of the incisions was measured. The data are in the le Nethea12 . csv. The columns are; 0 EField: 1 if the newt was in the control group, or 1.5 if the newt was in the treatment group, 0 HealDiff: Difference in healing rate in micrometres per hour (pm /h), where Difference = Treatment limb healing rate Control limb healing rate. (a) Provide a suitable graphical display that enables comparison of the distributions of healing rate differences for the two values of electric eld. [4] (b) Using a 5% signicance level, test the hypothesis that a 50% increase in the natural electric eld has no effect on the mean wound healing rate in newts. Take care to state and evaluate assumptions, qualify your conclusions appropriately, and describe any effect you find. [12]