Confidence intervals from small samplesAQA A-Level Further Maths: Flashcards

What these 13 flashcards ask

What is the interval for \mu with unknown variance and a small sample?
How many degrees of freedom for a one-sample t interval?
Which table column for a 95\% interval?
Which table column for a 99\% interval?
How does the t-distribution differ from the normal?
What happens to t critical values as n increases?
What assumption does the t interval need?
Why use t instead of z for a small sample?
Formula for the unbiased variance estimate?
A claimed mean lies outside the interval. What do you say?
A claimed mean lies inside the interval. What do you say?
How does a higher confidence level affect the interval?
What is the standard error with s=2.4 and n=8?

Exam questions on Confidence intervals from small samples

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
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
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

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).