4 A genetics researcher is investigating whether there is any association between natural hair colour and natural eye colour. A random sample of 800 adults is selected. Each adult can categorise their natural hair colour as blonde, brown, black or red and their natural eye colour as brown, blue or green.

1. Explain the benefit of using a random sample in this investigation. The data collected from the sample are summarised in Table 4.1. \begin{table}[h]
   \captionsetup{labelformat=empty} \caption{Table 4.1}

   \multirow{2}{*}{Observed frequency}		Hair Colour
   		Blonde	Brown	Black	Red	Total
   \multirow{3}{*}{Eye Colour}	Brown	47	153	196	36	432
   	Blue	61	78	115	26	280
   	Green	19	22	31	16	88
   	Total	127	253	342	78	800

   \end{table} The researcher decides to carry out a chi-squared test.
2. Determine the expected frequencies for each eye colour in the blonde hair category. You are given that the test statistic is 28.62 to 2 decimal places.
3. Carry out the chi-squared test at the 10\% significance level. Table 4.2 shows the chi-squared contributions for some of the categories. The contributions for the categories relating to green eye colour have been deliberately omitted. \begin{table}[h]
   \captionsetup{labelformat=empty} \caption{Table 4.2}

   Hair Colour \cline { 2 - 6 } Blonde Brown Black Red \multirow{3}{*}{ Eye Colour } Brown 6.791 1.964 0.694 0.889 \cline { 2 - 6 } Blue 6.162 1.257 0.185 0.062 \cline { 2 - 6 } Green \end{table} Calculate the chi-squared contribution for the green eye and blonde hair category. With reference to the values in Table 4.2, discuss what the data suggest about brown eye colour and blue eye colour for people with blonde hair. A different researcher, carrying out the same investigation, independently takes a different random sample of size 800 and performs the same hypothesis test, but at the 1\% significance level, reaching the same conclusion as the original test. By comparing only the significance level of the two tests, specify which test, the one at the 10\% significance level or the one at the 1\% significance level, provides stronger evidence for the conclusion. Justify your answer. This paper (6 questions) View full paper Q1 Q2 Q3 Q4 Q5 Q6