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.

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.

Using a random sample from a population with given mean and variance, find the expectation and variance of three estimators of $\mu$. Unbiased, efficient?

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

Arrivals given by exponential distribution, parameter $\theta$ and $Y$, sample mean on inter-arrival times. Find and calculate unbiased estimator for $\theta$.

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 Poisson distribution $\operatorname{Poisson}(\lambda)$ and given the mean of the sample, find the MLE for $\lambda$. Also find the expected information and a confidence interval for $\lambda$.

For a sample of size n from an Exponential distribution $\operatorname{Exponential}(\lambda)$  and given the mean of the sample, find the MLE for $\lambda$. Also find the expected information and a confidence interval for $\lambda$.

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.

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

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.

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

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

Normal distribution $X \sim  N(\mu,\sigma^2)$ given. Find $P(a \lt X \lt b)$. Find expectation, variance, $P(c \lt \overline{X} \lt d)$ for sample mean $\overline{X}$.

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.