Question

Lucy wants to know how her fourth-grade daughter, Monica, scored on a test of reading comprehension compared to the population of other fourth graders in the school district. Luckily, Lucy has taken this course and knows that a z-score will help her understand Monica’s reading score in relation to the population.

1. Calculate the obtained z-score by hand. Describe calculations
2. When alpha is set at .05, the critical value is ± 1.96. Should the null hypothesis be retained or rejected? Explain why.

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

Answer 1

Given that

Monica's reading comprehension score = 102,    Mean 4th reading comprehension score = 109    standard deviation of the 4th grade's reading comprehension = 2.8

so, x = 102, mu = 109 and sigma =2.8

z = (x-mu)/sigma

= (102-109)/2.8

= -7/2.8

= -2.5

We can see that the calculated z score for Monica's reading comprehension score is -2.5, which is outside the critical region of -1.96 and 1.96

So, we can reject the null hypothesis at 0.05 signficance level because z calculated value is in rejection region