For questions 8 & 9 use the following information. To receive full credit, you M
ID: 3217177 • Letter: F
Question
For questions 8 & 9 use the following information. To receive full credit, you MUST neatly write out each of the four steps we went through in class.: "The school psychologist at Wichita High School was interested in comparing the GPA of different groups of students to the mean GPA at her school. She found that the average GPA at the school was mu = 2.55 and sigma = .5." 8. She found that the average GPA of the 15 ESL (English as a Second Language) students was M = 2.76 with an S = .75. Were the GPAs of the ESL students significantly different from the overall school average? Test alpha = .05 two tailed.Explanation / Answer
Given that,
population mean(u)=2.55
standard deviation, =0.5
sample mean, x =2.76
number (n)=15
null, Ho: =2.55
alternate, H1: !=2.55
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 2.76-2.55/(0.5/sqrt(15)
zo = 1.62665
| zo | = 1.62665
critical value
the value of |z | at los 5% is 1.96
we got |zo| =1.62665 & | z | = 1.96
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value : two tailed ( double the one tail ) - ha : ( p != 1.62665 ) = 0.10381
hence value of p0.05 < 0.10381, here we do not reject Ho
ANSWERS
---------------
null, Ho: =2.55
alternate, H1: !=2.55
test statistic: 1.62665
critical value: -1.96 , 1.96
decision: do not reject Ho
p-value: 0.10381