Which of the following is a fundamental difference between the t statistic and a

Question

Which of the following is a fundamental difference between the t statistic and a z-score?

If a researcher is using a t statistic to test a null hypothesis about a population, what information is needed from the population to calculate the t statistic?

On average, what value is expected for the t statistic when the null hypothesis is true?

A sample of n = 4 scores has SS = 60. What is the variance for this sample?

A researcher conducts a (single sample) hypothesis test using a sample from an unknown population. If the t statistic has df = 30, how many individuals were in the sample?

What value is estimated with a confidence interval using the t statistic for single sample t-test? Which of the following would have no effect on the width of a confidence interval?

Explanation / Answer

t-statistic and Z-score differ in that the t-score is calculated using sample standard deviation in denominator while Z-score is calculated using population standard deviation in denominator.

t-statistics need population parameter mean under null hypothesis.

When null hypothesis is true, t-statistic is expected to be zero so that the null hypothesis is not rejected.

If n=4 and SS=60, variance=60/(4-1)=20

If df=30 then samle size =30+1=31

For single sample t-test the population parameter mean value is estimated using t-statistic.

Width of confidence interval is not affeted by the sample mean

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