Question

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).

Answer 1

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.