Interactive practice questions
In a sample of $350$350 people, it is found that only $1$1 has blood type B-negative.
Let $p$p represent the proportion of the population that have blood type B-negative.
Find an estimate for $p$p.
Find an approximate two-sided $95%$95% confidence interval for $p$p.
Give your answer as an interval in the form $\left(a,b\right)$(a,b), rounding all values to four decimal places.
Select the most appropriate interpretation of the confidence interval found in part (b).
We are $95%$95% confident that the probability that a person has blood type B-negative is contained within this interval.
The probability that a person has blood type B-negative is not contained within this interval.
The probability that a person has blood type B-negative is contained within this interval.
There is a $95%$95% chance that the probability that a person has blood type B-negative is contained within this interval.
One measure of the validity of a confidence interval is that the product of the sample size $n$n and the population proportion $p$p is greater than $5$5.
Estimate this product for the blood type sample.
Given the result of part (d), select the most appropriate statement below.
Since $np<5$np<5 for our estimate, we cannot be sure that the sampling distribution is approximately normal and so the confidence interval is not valid.
Since $np>5$np>5 for our estimate, we know that the sampling distribution is approximately normal and so the confidence interval is valid.
Jimmy works on the top floor of a $50$50 storey building. The probability that the elevator will stop at another floor on its way up to his office is $p$p.
Jimmy has decided to test this probability by noting the outcome for every one of the $236$236 working days of the year, over five years. He records a $1$1 if the elevator does stop, and a $0$0 if it doesn't stop.
The average outcome for each year is shown in the table below.
$30$30 hamburger patties advertised as being $180$180 g are weighed and the results are tabulated.
A supermarket is surveying individuals to determine what proportion is moving towards online grocery shopping. A random sample is taken of $205$205 people, and $80$80 people regularly shop online.