The following list shows three factors that can either increase or decrease the probability of a Type II error. The sample size is increased. The significance level is increased. The standard error is increased. Which factors alone will cause the probability of a Type II error to increase?

Answer:

Standard Error is increased.

Step-by-step explanation:

Type 2 error is failure to reject a false null hypothesis. This is a 'false negative' result of hypothesis testing, represented by beta 'β'.

Power of test is 1 - β, which shows probability of accurately stating  a null hypothesis false, when it is actually false.

Increased sample size increases the power of test accuracy, hence reduces type 2 error. Increased level of significance implies higher probability of rejecting a true null hypothesis, ie type 1 (false positive) error. So, it decreases type 2 error.

Standard Error increase implies lower level of t statistic , ie = (x - u) / (s / √ n) Lower the t value, higher is the probability of not rejecting null hypothesis, which implies higher chance of type 2 error.

Type II error is 1 - power of the test. The factor that can alone make the type II error to increase is: Option C: The standard error is increased.

Firstly the whole story starts from hypotheses. The null hypothesis is tried to reject and we try to accept the alternate hypothesis.

The probability of committing the type I error is called the significance level of the hypothesis test.

And the more we increase the level of significance, the less area the test statistic gets to fall in, and its chances of falling in region outside level of significance increases, which makes us to reject the null hypothesis more probable, thus, decreasing its chance of tagging as negative, not mattering if true or false.
Thus, increasing level of significance increases the type I error but decreases the type II error.

If it is increases, the likely area for test statistic falling increases, thus, increasing probability of tagging the null hypothesis tagging to be true, so increasing result of test being declared negative, thus, increasing type II error.

Increasing sample size increases statistical power, thus, decreasing the type II error.

Thus, for the given case, as the sampling size is increased, the type II error will decrease, as the significance level is increased, the type II error will decrease, and as the standard error is increased, the type II error will increase with it.

Thus, out of the given factors, only the last factor (increasing the standard error) makes the type II error to get increased.

Thus, the factor that can alone make the type II error to increase is: Option C: The standard error is increased.

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