Paired t-test to see if there is a difference between times take in a task.

Application of the Poisson distribution given expected number of events per interval.

Finding probabilities using the Poisson distribution.

rebelmaths

rebelmaths

Application of the binomial distribution given probabilities of success of an event.

Finding probabilities using the binomial distribution.

Two sample t-test to see if there is a difference between scores on questions between two groups when the questions are asked in a different order.

Given normal distribution $\operatorname{N}(m,\sigma^2)$ find $P(a \lt X \lt b),\; a \lt m,\;b \gt m$ and also find the value of $X$ corresponding to a given percentile $p$%. 

Two sample t-test to see if there is a difference between scores on questions between two groups when the questions are asked in a different order.

An experiment is performed twice, each with $5$ outcomes

$x_i,\;y_i,\;i=1,\dots 5$ . Find mean and s.d. of their differences $y_i-x_i,\;i=1,\dots 5$.

Application of the Poisson distribution given expected number of events per interval.

Finding probabilities using the Poisson distribution.

Application of the binomial distribution given probabilities of success of an event.

Finding probabilities using the binomial distribution.

Application of the Poisson distribution given expected number of events per interval.

Finding probabilities using the Poisson distribution.

Application of the binomial distribution given probabilities of success of an event.

Finding probabilities using the binomial distribution.

Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

Given sample data find mean, standard deviation, median, interquartile range.

Note that there are different versions of the upper and lower quartiles, so you may want to include your own versions - see the user defined functions in the question.

Two sample t-test to see if there is a difference between scores on questions between two groups when the questions are asked in a different order.

Given mean and sd of 1000 sample returns on a scale of 1 to 7 together with a given score, find the z-score.

Also find the 95% confidence interval for the population mean.

One-way ANOVA example

Given data on population mean and population standard deviation and three sampling sizes, calculate the probabilities that the sample means are within a specified distance from the population mean.

For a sample of size n from a normal distribution, given mean of the sample mean and the standard deviation , find the t-statistic corresponding to a null hypothesis $\mu=m$ and a given confidence level. Check if the result is significant at this level.

LSD and Tukey yardsticks on three treatments. Also one-way Anova test on same set of data.

Paired t-test to see if there is a difference between times take in a task.

Given sample data find mean, standard deviation, median, interquartile range,

One-way ANOVA example

Given 32 datapoints in a table find their minimum, lower quartile, median, upper quartile, and maximum.

Sample of size $24$ is given in a table. Find sample mean, sample standard deviation, sample median and the interquartile range.

Two ordered data sets, each with 10 numbers. Find the sample standard deviation for each and for their sum.

Provided with information on a sample with sample mean and standard deviation, but no information on the population variance, use the t test to either accept or reject a given null hypothesis.

Two ordered data sets, each with 10 numbers. Find the sample standard deviation for each and for their sum.

Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

Given three linear combinations of four i.i.d. variables, find the expectation and variance of these estimators of the mean $\mu$. Which are unbiased and efficient?

Given 32 datapoints in a table find their minimum, lower quartile, median, upper quartile, and maximum.