MATH SOLVE

4 months ago

Q:
# For sample sizes greater than 40, the results of hypothesis tests and confidence intervals using the t distribution are highly sensitive to non-normality of the population from which samples are takenb.the use of the t distribution assumes that the population from which the sample is drawn is normally distributedc.for small sample sizes, the t distribution should not be used for data that is highly skewed and/or contains extreme outliersd.since the t distribution procedure is robust, it can be used even for small sample with strong skewness and extreme outliers

Accepted Solution

A:

We' supposed to indicate which statement is true/false.

Note that, if a sample size is 40 or over, we can use the t distribution even with skewed data. So it's not highly sensitive to non-normality of the population from which samples are taken. So statement A is false.

It's true that the t-distribution assumes that the population from which samples are drawn is normally distributed. So B is true.

For skewed data or with extreme outliers, we can't use the t distribution. We only use t distribution as long as we believe that the population from which samples are drawn is closed to a bell-shape. So C is true.

Lastly, statement D is against statement C. So D is false.

Note that, if a sample size is 40 or over, we can use the t distribution even with skewed data. So it's not highly sensitive to non-normality of the population from which samples are taken. So statement A is false.

It's true that the t-distribution assumes that the population from which samples are drawn is normally distributed. So B is true.

For skewed data or with extreme outliers, we can't use the t distribution. We only use t distribution as long as we believe that the population from which samples are drawn is closed to a bell-shape. So C is true.

Lastly, statement D is against statement C. So D is false.