Question-63

Hypothesis Testing

Consider the following situation and match them with suitable test statistics and hypothesis test:

Suppose we observe samples from a normal distribution, where the variance is unknown. We want to check whether the variance is greater than \(\sigma^2\). What test statistic and test can be applied to this situation\(?\)

Test Statistic: \(T\) = Sample mean, Hypothesis test: \(t\)-test.
Test Statistic: \(T\) = Sample mean, Hypothesis test: \(\chi^2\)-test.
Test Statistic: \(T\) = Sample variance, Hypothesis test: \(\chi^2\)-test.
Test Statistic: \(T\) = Sample variance, Hypothesis test: \(F\)-test.

Hint

Hupothesis will be :

\(H_0 :\) Population variance will be equal to \(\sigma^2\).

\(H_1 :\) Population variance is greater than \(\sigma^2\).

Based on this information, choose the correct option.

Answer

Test Statistic: \(T\) = Sample mean, Hypothesis test: \(t\)-test.
Test Statistic: \(T\) = Sample mean, Hypothesis test: \(\chi^2\)-test.
Test Statistic: \(T\) = Sample variance, Hypothesis test: \(\chi^2\)-test.
Test Statistic: \(T\) = Sample variance, Hypothesis test: \(F\)-test.

Solution