Question

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 taken
b.the use of the t distribution assumes that the population from which the sample is drawn is normally distributed
c.for small sample sizes, the t distribution should not be used for data that is highly skewed and/or contains extreme outliers
d.since the t distribution procedure is robust, it can be used even for small sample with strong skewness and extreme outliers

Answer 1

$\boxed{{\text{Option b}}}$ is correct as the the use of the t distribution assumes that the population from which the sample is drawn is normally distributed.

$\boxed{{\text{Option c}}}$ for small sample sizes, the t distribution should not be used for data that is highly skewed and/or contains extreme outliers.

Further Explanation:

For sample sizes greater than $40$.

a) 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 taken is not correct as the sample size is large the data is normally distributed.

b) the use of the t distribution assumes that the population from which the sample is drawn is normally distributed is correct as the condition to apply t-distribution is that the data is normally distributed.

c) for small sample sizes, the t distribution should not be used for data that is highly skewed and/or contains extreme outliers is correct as the sample size is small the data set is less normally distributed.

d) since the t distribution procedure is robust, it can be used even for small sample with strong skewness and extreme outliers is not correct as it is the contradiction of option (c).

$\boxed{{\text{Option b}}}$ is correct as the the use of the t distribution assumes that the population from which the sample is drawn is normally distributed.

$\boxed{{\text{Option c}}}$ for small sample sizes, the t distribution should not be used for data that is highly skewed and/or contains extreme outliers.

Learn more:

1. Learn more about normal distribution brainly.com/question/12698949

2. Learn more about standard normal distribution brainly.com/question/13006989

Answer details:

Grade: College

Subject: Statistics

Chapter: Normal distribution

Keywords: Z-score, Z-value, standard normal distribution, standard deviation, criminologist, test, measure, probability, low score, mean, repeating, indicated, normal distribution, percentile, percentage, undesirable behavior, proportion.

Answer 2

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.