Given a normal distribution $X \sim N(m,\sigma^2)$ find $P(X \lt a),\; a \lt m$ and the conditional probability $P(X \gt b | X \gt c)$ where $b \lt m$ and $c \gt m$.

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 $y_i-x_i,\;i=1,\dots 5$.

Given two sets of data, sample mean and sample standard deviation, on performance on the same task, make a decision as to whether or not the mean times differ. Population variance not given, so the t test has to be used in conjunction with the pooled sample standard deviation.

Link to use of t tables and p-values in Show steps.

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

Finding probabilities using the binomial distribution.

Paired t-test to see if there is a difference between responses after treatment.

Testing an hypothesis about the mean of one group.

Testing an hypothesis about the mean of one group.

Calculating summary statistics.

Paired t-test to see if there is a difference between responses after treatment.

A comparison of the means of four groups.

A comparison of the means of three groups.

A comparison of the means of three groups.

A comparison of the mean of two groups.

A comparison of the mean of two groups.

A comparison of the mean of two groups.

A comparison of the mean of two groups.