Question

The average age of students at the University of Houston – Downtown is about 28 years old. The president of the university believes that the age of full-time students attending classes during the day is lower that the average of all students. Test this hypothesis. Be sure to show all five steps.

Show your Excel file ONCE per group with all the names of your team members included.

Age

14-21: 23%

22-24: 23%

25-30: 27%

31-35: 12%

36-50: 13%

Over 50: 2%

Answer 1

Lower	Upper	Xi = (Li+Ui)/2	Pi	Xi*Pi	Xi^2*Pi
14	21	17.5	23%	4.025	70.4375
22	24	23	23%	5.29	121.67
25	30	27.5	27%	7.425	204.1875
31	35	33	12%	3.96	130.68
36	50	43	13%	5.59	240.37
51	75	63	2%	1.26	79.38
sum			100%	27.55	846.73

Mean= sum(Xi*Pi)
27.55

var= sum(Xi^2*Pi)-mean^2
87.72

sd = sqrt(var)
9.37

step 1:

Consider the null hypothesis, Ho: the average age is 28 years old. This is tested against an alternative hypothesis, the average age is not 28 years old.

step 2:

mean= 27.55
sd= sqrt(var) 9.37
u= 28.00
n= 100.00
alpha= 0.05

step 3:

critical value: z(a/2)
z(0.05/2)
1.960

step 4: test statistic,

z = (mean-u)/(sd/sqrt(n))
= (27.55-28)/(9.37/sqrt(100))
-0.4803

p-value
2*(1-P(z<|z|)
2*(1-P(z<abs(-0.4803))
normsdist(abs(-0.4803))
0.6310

step 5:

with z=00.48, p-value > 5%, i fail to reject the null hypothesis and conclude that the average age is not 28 years old.