The Trial Urban District Assessment (TUDA) is agovernment-sponsored study of student achievement inlarge urban school districts. TUDA gives a mathematicstest scored from 0 to 500. A score of 262 is a "basic"mathematics level, and a score of 299 is "proficient."Scores for a random sample of 1100 eighth-graders inDallas had x = 264 with standard error 1.3.TUDA results for 2019 from the National Center for Education Statistics, athttps://www.nationsreportcard.gov.O Macmillan Learning(a) We don't have the 1100 individual scores, but useof the t procedures is surely safe. Why?O Because the data has a strong skew.O Because the sample size is very large.O Because use of the t procedures is always safe.O Because the sample doesn't have outliers.

In this case, a mathematics test score of all students ranging from 0 to 500 is considered as the population distribution.The random sample of 1100 eighth-graders has a sample average score of x¯=264 and a standard error value of 1.3.Essentially, using the central limit theorem (CLT), the sampling distribution of the sample average is theoretically interpreted to be distributed normally with centered around the population mean, if the sample size is suffiiently large (i.e., the sample size, n≥30) regardless of the skewed nature of the parent (or population) distribution.In this case, as the sample number of students of 1100 is sufficiently large, i.e., n(=1100)>30, the sampling distribution of the average math score for 1100 sampled eighth-graders is considered to be theoretically distributed normally irrespective of the distribution of the math score at the population level. Due to the extremely large sample size, the t-distribution is desired. The second option is correct.As no additional information regarding the nature of the distribution of the scores is given, a skewed nature of the math score can not be interpreted. Thus the first option is rejected.Interpreting the sampling distribution of sample averages with a lower sample size and no prior information regarding the normality of the distribution at the population level, the use of t-distribution is not safe. Thus the third option is rejected.Considering each of the individual sample scores is not specified, no extremely high or small values from the general observation of test scores are interpreted. Thus the fourth option is rejected.Use of the t-procedure is surely safe "because the sample size is very large". The second option is correct.