a. Is the age of biology students significantly different from all college stude

Question

a. Is the age of biology students significantly different from all college students?Assume that there is a normal distribution.Show your calculations and cite the correct critical value.

The average age of all college students is 22.62, =1.42, N=2210. The average age of biology students is 20.87, s=1.56, n=22.

B- How is the age of biology students different than the age of all college students?

-Significantly higher -Significantly lower-No significant difference -Don’t know from this data

c. Given the values below, derivate the effect size; what exact sample mean (x = ?) will make a

significant difference? Show your calculations.

Critical value = 2.365 = 150=2.5N=8

Explanation / Answer

PART A.
Given that,
population mean(u)=22.62
standard deviation, =1.42
sample mean, x =20.87
number (n)=22
null, Ho: =22.62
alternate, H1: !=22.62
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 = 20.87-22.62/(1.42/sqrt(22)
zo = -5.78044
| zo | = 5.78044
critical value
the value of |z | at los 5% is 1.96
we got |zo| =5.78044 & | z | = 1.96
make decision
hence value of | zo | > | z | and here we reject Ho
p-value : two tailed ( double the one tail ) - ha : ( p != -5.78044 ) = 0
hence value of p0.05 > 0, here we reject Ho
ANSWERS
---------------
null, Ho: =22.62
alternate,age of biology students significantly different from all college students H1: !=22.62
test statistic: -5.78044
critical value: -1.96 , 1.96
decision: reject Ho
p-value: 0

we claim that age of biology students significantly different from all college students

PART B.
Significantly lower

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