4.16 Confidence intervalsIB Maths: Applications and Interpretation HL: Flashcards

What these 13 flashcards ask

Formula for a confidence interval for \mu when \sigma is known?
Formula for a confidence interval for \mu when \sigma is unknown?
Critical z values for 90\%, 95\% and 99\% confidence?
When do you use the t-distribution?
Degrees of freedom for a one-sample t-interval?
Which estimate of the standard deviation do you use for a t-interval?
How does a higher confidence level change the interval?
How does a larger sample size change the interval?
What does a 95\% confidence level mean?
A claimed mean lies outside the interval. What can you say?
A claimed mean lies inside the interval. What can you say?
How do you find the sample size for a given margin E?
How do you find \bar{x} from an interval (a,\ b)?

Exam questions on 4.16 Confidence intervals

The masses of cats of a certain breed are normally distributed with a known standard deviation of $0.6$ kg. A random sample of $25$ of these cats has a mean mass of $4.20$ kg. A confidence interval is to be found for the population mean mass $\mu$ .
The breed society claims that the mean mass of these cats is $4.5$ kg. Use your interval from (b) to comment on this claim.2 marks
The lifetimes, in hours, of a type of battery are normally distributed with unknown mean $\mu$ and unknown standard deviation. The lifetimes of a random sample of $12$ batteries are: $40.2,\ 38.9,\ 41.5,\ 39.8,\ 42.1,\ 40.7,\ 39.3,\ 41.0,\ 40.4,\ 38.6,\ 41.8,\ 40.2$ . Use your GDC where helpful.
Use your GDC to find a $95\%$ confidence interval for $\mu$ .2 marks
The daily screen time of teenagers, in minutes, is normally distributed with a known standard deviation. A $95\%$ confidence interval for the population mean $\mu$ , based on a random sample of $64$ teenagers, is $(152.65,\ 167.35)$ .
(i) Write down the sample mean. (ii) Find the value of the population standard deviation.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).