Calculate and work with measures of central tendency such as mean, median and mode, and measures of spread such as range and standard deviation.

No description given

No description given

Integrate $f(x) = ae ^ {bx} + c\sin(dx) + px^q$. Must input $C$ as the constant of integration.

Calculate and work with measures of central tendency such as mean, median and mode, and measures of spread such as range and standard deviation.

This question shows how to ask for a number in scientific notation, by asking for the significand and exponent separately and using a custom marking algorithm in the gap-fill part to put the two pieces together.

Answers not in standard form, i.e. with a significand not in $[1,10)$, are accepted but given partial marks.

Convert a variety of numbers from decimal to standard index form.

6 questions on standard statistical distributions.

Binomial, Poisson, Normal, Uniform, Exponential.

Compute the standard error of a sample mean, given the sample size and standard deviation.

Just showing how to use the stdev function from the stats extension to calculate the standard deviation of a list of numbers.

rebelmaths

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

For a sample of size n from a normal distribution and given the mean of the sample and the standard deviation of the distribution, find the MLE for the mean. Also the expected information and a confidence interval for the 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.

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.

6 questions on standard statistical distributions.

Binomial, Poisson, Normal, Uniform, Exponential.

Let $P_n$ denote the vector space over the reals of polynomials $p(x)$ of degree $n$  with coefficients in the real numbers.

Let the linear map $\phi: P_4 \rightarrow P_4$ be defined by:

$\phi(p(x))=ap(x) + (bx + c)p'(x) + (x ^ 2 + dx + f)p''(x)$

Using the standard basis for range and domain find the matrix given by $\phi$.

Let $P_n$ denote the vector space over the reals of polynomials $p(x)$ of degree $n$  with coefficients in the real numbers. Let the linear map $\phi: P_4 \rightarrow P_4$ be defined by: \[\phi(p(x))=p(a)+p(bx+c).\]Using the standard basis for range and domain find the matrix given by $\phi$.

6 questions on standard statistical distributions.

Binomial, Poisson, Normal, Uniform, Exponential.

6 questions on standard statistical distributions.

Binomial, Poisson, Normal, Uniform, Exponential.

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.

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.

Finding the confidence interval at either 90%, 95% or 99% for the mean given the mean and standard deviation of a sample. The population variance is not given and so the t test has to be used. Various scenarios are included.

Questions which rely on knowledge of standard integrals.

6 questions on standard statistical distributions.

Binomial, Poisson, Normal, Uniform, Exponential.