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

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?

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

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

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

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

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

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

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 stratified sampling, the population is divided into:

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

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

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

Heteroscedasticity in a regression model means:

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

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

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

The power of a statistical test is:

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

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

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

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

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

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

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

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

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

Perfect multicollinearity in a multiple regression model means:

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

Which measure of dispersion is least affected by extreme observations?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

In hypothesis testing, a Type II error occurs when:

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

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

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

The Durbin-Watson statistic is primarily used to detect:

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

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

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

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

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

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