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.

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.

A weighted coin with given $P(H),\;P(T)$ is tossed 3 times. Let $X$ be the random variable which denotes the longest string of consecutive heads that occur during these tosses. Find the Probability Mass Function (PMF), expectation and variance of $X$.

Deciding whether or not  three sampling methods are simple random sampling, stratified sampling, systematic or judgemental sampling. Also whether or not the method of selection is random, quasi-random or non-random.

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.

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

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

Given sum of sample from a Normal distribution with unknown mean $\mu$ and known variance $\sigma^2$. Find MLE of $\mu$ and one of four functions of $\mu$.

Given a PDF $f(x)$ on the real line with unknown parameter $t$ and three random observations, find log-likelihood and MLE $\hat{t}$ for $t$. 

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.

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 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 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.

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

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

A box contains $n$ balls, $m$ of these are red the rest white.

$r$ are drawn without replacement.

What is the probability that at least one of the $r$ is red?

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

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

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.

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

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

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 $\overline{X}$.

Three parts. A sample of size $n$ is taken from $N$ where $k$ of the items are known to be defective and the task is to find the probability that more than $m$ defectives are in the sample. First part is sampling with replacement (binomial), second is sampling without replacement, (hypergeometric) and the last part uses the Poisson approximation to the first part.

Given subset $T \subset S$ of $m$ objects in $n$ find the probability of choosing without replacement $r\lt n-m$ from $S$ and not choosing any element in $T$.

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.