It is impossible for the standard error to have a value larger than the standard

Question

It is impossible for the standard error to have a value larger than the standard deviation of the population from which the sample is selected._ If a researcher is predicting that a treatment will produce an increase in scores, then the critical regiorn for a directional test would be located entirely in the left-hand tail of the distribution. Changing alpha from .05 to .01 increases the risk of a Type I error. As the sample variance increases, the value for the t statistic also increases. (Assume all other factors are held constant.). For a two-tailed hypothesis test with = .05 using a sample of n = 20 scores, the critical values for t would be 1 = +/-2.086. For a one-tailed test with = .01 using a sample of n = 16, the critical value for t would be 2.602.

Explanation / Answer

Answers

1. True. Standard error is obtained by dividing the population standard deviation by the sample size and so, SE < SD

2. False. Since the researcher is expecting an increase, the alternative hypothesis would be µ > µ0 and hence the critical value will be on the right tail.

3. False. Level of significance, is the probability of committing type I error. So, changing from 0.05 to 0.01 would, in fact, reduce the risk of committing type I error.

4. False. t-statistic has the sample standard deviation in the denominator and so when variance and hence standard deviation increases, the value of t-statistic would reduce.

DONE

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