In: Statistics and Probability
Monica's reading comprehension score = 102, Mean 4th reading comprehension score = 109 standard deviation of the 4th grade's reading comprehension = 2.8 Monica's z-score in math = 1.3 Mean 4th grade math score= 218 Standard deviation of the 4th grades scores = 12.2 State the dependent variable. Explain whether Lucy should use a one-tailed or a two-tailed z-test and explain why. Calculate the obtained z-score by hand. Describe your calculations (i.e., show your work).
The dependent variable is Monica's test scores in reading comprehension and Math.
Lucy can use one tailed z-test because Monica's reading comprehension score = 102 is less than Mean 4th grade reading comprehension score = 109.
Z-score =
where X = score in corresponding test
population mean = 109
= population standard deviation = 2.8
Z-score for reading comprehension score = = -2.5
For math score Z-score is given Z = 1.3
corresponding math score = Mean 4th grade math score +Z* Standard deviation of the 4th grade math scores
= 218 + 1.3*12.2 = 233.86 = 234.
For this math score Lucy can use one tailed z-test because Monica's math score is more than Mean 4th grade math score = 218 claim for this case will be monica's math score is more than mean 4th grade math score.