Confidence intervals from small samplesAQA A-Level Further Maths: Mind map

Exam questions on Confidence intervals from small samples

1. The masses of chocolate bars from a production line are normally distributed. A random sample of $8$ bars has sample mean $36.2$ g and an unbiased estimate of the population standard deviation of $2.4$ g.
   The $0.5\%$ critical value of $t$ with $7$ degrees of freedom is $3.499$. Find a $99\%$ confidence interval for the population mean mass.2 marks
2. The battery life, in hours, of a make of phone is normally distributed. A random sample of $12$ phones has $\sum x=220.8$ and $\sum x^2=4087.47$.
   The manufacturer claims that the mean battery life is $20$ hours. Use your interval from (b) to comment on this claim.2 marks
3. The reaction times, in milliseconds, of a random sample of $7$ drivers are $248,\ 262,\ 255,\ 241,\ 270,\ 259,\ 253$. Reaction times may be assumed to be normally distributed.
   Calculate the sample mean and an unbiased estimate of the population variance.3 marks