Respuesta :
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.
[tex]\boxed{{\text{Option b}}}[/tex] is correct as the the use of the t distribution assumes that the population from which the sample is drawn is normally distributed.
[tex]\boxed{{\text{Option c}}}[/tex] 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 [tex]40[/tex].
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).
[tex]\boxed{{\text{Option b}}}[/tex] is correct as the the use of the t distribution assumes that the population from which the sample is drawn is normally distributed.
[tex]\boxed{{\text{Option c}}}[/tex] 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 https://brainly.com/question/12698949
2. Learn more about standard normal distribution https://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.
