Which statistic is sufficient for μ when X1,...,Xn are independent N(μ,σ²) observations with known σ²?

The moment generating function of a Poisson distribution with parameter λ is:

Which condition is required for the classical one-way ANOVA F-test?

If X follows a binomial distribution with n=10 and p=0.3, what is Var(X)?

Heteroscedasticity in a regression model means:

A sample of size 25 has mean 80 and standard deviation 10. What is the standard error of the sample mean?

If X~Exponential(λ), its memoryless property is represented by:

Perfect multicollinearity in a multiple regression model means:

If a statistical test rejects H0 when the test statistic falls in the rejection region, the probability of this event under H0 is called:

If a population has variance 25 and a random sample of size 100 is taken, what is the standard deviation of the sampling distribution of the sample mean?

In hypothesis testing, a Type II error occurs when:

A test has significance level α=0.05. If the null hypothesis is true, the probability of rejecting it is:

For a continuous random variable X, P(X=a) is:

For an exponential distribution with rate λ, the coefficient of variation is:

If the regression coefficients are byx=0.6 and bxy=0.4, what is the correlation coefficient?

In stratified sampling, the population is divided into:

Which estimator has the smallest variance among all unbiased estimators of a parameter, if it satisfies the relevant regularity conditions and attains the Cramér-Rao lower bound?

In a chi-square goodness-of-fit test, expected frequencies are calculated under:

If X~Binomial(n,p), its probability generating function is:

For a contingency table with r rows and c columns, the degrees of freedom for a chi-square test of independence are:

For a normal population with unknown variance, the statistic (X̄-μ)/(S/√n) follows:

For any random variable X with finite variance, which inequality always holds?

For a t-distribution with ν degrees of freedom, as ν tends to infinity, the distribution approaches:

For a positively skewed distribution, the usual relationship among mean, median and mode is:

A population consists of 60% males and 40% females. If a sample is selected with exactly the same proportions, the sampling method is most appropriately described as:

In multiple linear regression, the adjusted R² differs from R² because it:

If two variables X and Y have correlation coefficient -0.8, what is the correlation coefficient between 3X+5 and -2Y+7?

Which distribution is the exact sampling distribution of the sample variance, after suitable scaling, for a normal population?

The Cramér-Rao lower bound provides a lower bound for the variance of:

Which sampling method gives every possible sample of a specified size an equal probability of selection?

If a random sample of size n is drawn from a population with variance σ², the variance of the sample mean is:

If the first four central moments are μ1=0, μ2=4, μ3=0 and μ4=48, the coefficient of kurtosis β2 is:

Which transformation is most commonly used to stabilize variance in count data with Poisson-like characteristics?

If the regression lines are y=2x+3 and x=0.5y-1, what is the correlation coefficient?

Which measure of dispersion is least affected by extreme observations?

If SST=500 and SSE=200 in a one-way ANOVA, what is the coefficient of determination?

The power of a statistical test is:

According to the Central Limit Theorem, under broad conditions, the distribution of the sample mean approaches:

The null hypothesis in a chi-square test of independence states that:

For a Poisson random variable X with mean 4, what is P(X=2)?

A 95% confidence interval for a population mean becomes narrower when:

If the coefficient of variation of a distribution is 20% and its mean is 50, what is its standard deviation?

If X~N(μ,σ²), the standardized variable Z is:

A normal distribution has mean 100 and standard deviation 15. Approximately what percentage of observations lie between 70 and 130?

If X and Y are independent random variables, which statement is necessarily true?

For a chi-square distribution with ν degrees of freedom, its mean is:

If X has mean 10 and variance 16, what is E[(X-10)²]?

Which distribution is commonly used as the sampling distribution of the ratio of two independent sample variances from normal populations?

If X is a random variable with E(X)=5 and Var(X)=9, what is Var(4X-7)?

If the odds in favour of an event are 3:2, what is the probability of the event?

The Durbin-Watson statistic is primarily used to detect:

If X follows a standard normal distribution, what is P(X>0)?

If two variables have Pearson correlation r=0, which conclusion is necessarily valid?

If a distribution has skewness coefficient zero and kurtosis coefficient equal to 3, it is characteristic of:

The likelihood principle implies that statistical inference about a parameter should depend on:

In systematic sampling with population size N=1000 and sample size n=100, the sampling interval is:

If the p-value is 0.03 and α=0.05, the appropriate decision is:

If the covariance between X and Y is 12, σX=3 and σY=8, the correlation coefficient is:

If the confidence level is increased from 95% to 99%, the corresponding confidence interval generally:

Which estimator is unbiased for the population variance when sampling is from a normal population?