Question 2 - A-Level Maths

Write down the approximate distribution of the sample mean height. Give a reason for your answer.
Hence find the probability that the sample mean height is at least 91 cm . \item A biologist investigated whether or not the diet of chickens influenced the amount of cholesterol in their eggs. The cholesterol content of 70 eggs selected at random from chickens fed diet \(A\) had a mean value of 198 mg and a standard deviation of 47 mg . A random sample of 90 eggs from chickens fed diet \(B\) had a mean cholesterol content of 201 mg and a standard deviation of 23 mg .
Stating your hypotheses clearly and using a \(5 \%\) level of significance, test whether or not there is a difference between the mean cholesterol content of eggs laid by chickens fed on these two diets.
State, in the context of this question, an assumption you have made in carrying out the test in part (a). \item The table below shows the price of an ice cream and the distance of the shop where it was purchased from a particular tourist attraction. \end{enumerate}
Shop Distance from tourist attraction (m) Price (£)
A 50 1.75
B 175 1.20
C 270 2.00
D 375 1.05
E 425 0.95
F 580 1.25
G 710 0.80
\(H\) 790 0.75
I 890 1.00
J 980 0.85
Find, to 3 decimal places, the Spearman rank correlation coefficient between the distance of the shop from the tourist attraction and the price of an ice cream.
Stating your hypotheses clearly and using a \(5 \%\) one-tailed test, interpret your rank correlation coefficient.

Shop	Distance from tourist attraction (m)	Price (£)
A	50	1.75
B	175	1.20
C	270	2.00
D	375	1.05
E	425	0.95
F	580	1.25
G	710	0.80
\(H\)	790	0.75
I	890	1.00
J	980	0.85