Question

In: Statistics and Probability

1. If other factors are held constant, what is the effect of decreasing the variability of...

1. If other factors are held constant, what is the effect of decreasing the variability of scores in a sample (i.e., decreasing a sample variance or standard deviation)? Hint: Look at the formulas for the estimated standard error and t-test for a single sample to figure out the answer.

A. It will increase the estimated standard error and decrease the likelihood of rejecting H0.

B. It will increase the estimated standard error and increase the likelihood of rejecting H0.

C. It will decrease the estimated standard error and decrease the likelihood of rejecting H0.

D. It will decrease the estimated standard error and increase the likelihood of rejecting H0.

2. If other factors are held constant, what is the effect of decreasing the sample size? (Hint: Look at the formulas for the estimated standard error and t-test for a single sample to figure out the answer).

A. It will decrease the estimated standard error and increase the likelihood of rejecting H0.

B. It will decrease the estimated standard error and decrease the likelihood of rejecting H0.

C. It will increase the estimated standard error and increase the likelihood of rejecting H0.

D. It will increase the estimated standard error and decrease the likelihood of rejecting H0.

Solutions

Expert Solution

1 ) As the variability decreases , In sample variance is also decrease as sample variance is decrease esmiated sample variance is also decrease because it is unbiased estimator . So as estimated sample variance decrease the likelihood increase because likelihood is probability of obtaining random sample given parameters decreases likelihood also increases since probability increases. So t statistic is also increasing and there is more chances of rejecting null hypothesis.So I think

It will decrease the estimated standard error and increase the likelihood of rejecting Ho .

2) . As sample size decreases the standard deviation will be increase so estimated standard error also increase because it is asn unbiased estimator.So as sample size decreases likelihood also decreases.

So I think It will increase the estimated standard error and decrease the likelihood of rejecting Ho .

orchestra answered 2 years ago
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