Question

Listed below are ages of actresses and actors at the time that they won an award for the categories of Best Actress and Best Actor. Use the sample data to test for a difference between the ages of actresses and actors when they win the award. Use a 0.05 significance level. Assume that the paired sample data is a simple random sample and that the differences have a distribution that is approximately normal.

Actress' age

18, 26, 30, 59, 32

Actor's Age

44, 49, 62, 55, 44

Identify the test statistic by filling in the blanks.

t=____

​(Round to two decimal places as​ needed.)

Identify the​ P-value.

​P-value=____

​(Round to three decimal places as​ needed.)

What is the conclusion based on the hypothesis​ test?

Since the​ P-value is ________ (greater or less) than the significance​ level,

we ___________ (fail to reject or reject) the null hypothesis. There ______(is, or is not) sufficient evidence to support the claim that there is a difference between the ages of actresses and actors when they win the award.

Answer 1

x= actress age when they won the award

y= actors age when they won the award

We want to test that the difference between the ages when an actor or actress won the award.

u1:- mean of the actress when they won the award.

u2:- mean age of actor when they won the award.

Ho: u1-u2 = 0 vs Ha:- u1 - u2 # 0

Sr.No	X	X-M1	(X-M1)^2	Y	Y-M2	(Y-M2)^2
1	18	-15	225	44	-6.8	46.24
2	26	-7	49	49	-1.8	3.24
3	30	-3	9	62	11.2	125.44
4	59	26	676	55	4.2	17.64
5	32	-1	1	44	-6.8	46.24
Total	165		960	254		238.8
M1= total/ 5	33		M2 = total/5	50.8

for the actress

N1: 5
df1 = N - 1 = 5 - 1 = 4
M1: 33
SS1: 960
s21 = SS1/(N - 1)

= 960/(5-1)

= 240

for the actors

N2: 5
df2 = N - 1 = 5 - 1 = 4
M2: 50.8
SS2: 238.8
s22 = SS2/(N - 1)

= 238.8/(5-1)

= 59.7

df = n1+n2 - 2 = 5+5-2 = 8

s2p = ((df1/(df1 + df2)) * s21) + ((df2/(df2 + df2)) * s22)

= ((4/8) * 240) + ((4/8) * 59.7)

= 149.85

s2M1 = s2p/N1 = 149.85/5 = 29.97
s2M2 = s2p/N2 = 149.85/5 = 29.97

The test statistics value :
t = (M1 - M2)/√(s2M1 + s2M2)

= -17.8/√59.94

t= -2.3

t = -2.3

P-value = P( |tdf  | > |t| )

=2*P( t8 > 2.3 )

= 2* 0.0252

= 0.0504

P-value = 0.0504

level of significane = 0.05

Since the​ P-value is greater than the significance​ level,

we fail to reject the null hypothesis. There is not sufficient evidence to support the claim that there is a difference between the ages of actresses and actors when they win the award.