# Quantitative Methods for Accounting & Finance

Added on  2023-06-04

8 Pages1656 Words306 Views
|
|
|
Quantitative Methods for Accounting & Finance
Answer 1
Part a)
Sample size n = 16, population mean μ=1000 and population standard deviation σ=200
i.
P ( X

>1050 ) =P
( X

μ
σ
n
>1050μ
σ
n )=P
( Z >10501000
200
16 ) =P ( Z >1 ) =1P ( Z1 )
Now, P ( Z1 ) =0 . 8413 implies that P ( X

>1050 ) =0 .1587
ii.
P ( 960< X

<1050 )=P
( 960μ
σ
n
< X

μ
σ
n
<1050μ
σ
n ) =P
( 9601000
200
16
<Z <10501000
200
16 )
P ( 960< X

< 1050 )=P ( 0 . 8< Z< 1 ) =P ( Z <1 ) P ( Z<0 .8 ) =P ( Z <1 ) + P ( Z < 0. 8 ) 1
Again, P ( Z0. 8 ) =0 .7881 implied that P ( 960< X

< 1050 )=0 . 8413+0 . 78811=0. 6294
Part b)
Let X denotes the length of the subcomponent, where X ~ N ( 117 ,(5. 2 )2 )
i. Required probability
P ( X >120 ) =P ( Xμ
σ >120μ
σ )=P ( Z >120117
5 . 2 )=P ( Z> 0. 58 )
=> P ( X >120 ) =P ( Z >0 . 58 ) =1P ( Z0 . 58 ) =10 .719=0 .281
Hence, required probability for one selected subcomponent to be longer than 120 cm is
0.281.
ii. Let X denotes the average length of four subcomponents.
Then, the required probability is,
P ( X

>120 ) =P
( X

μ
σ
n
>120μ
σ
n )=P
( Z >120117
5 . 2
4 )=P ( Z>1. 15 ) =1P ( Z1 .15 )
=> P ( X

>120 ) =1P ( Z1 .15 ) =10 . 8749=0 . 1251
Hence, the probability of mean length of four subcomponents exceeding 120cm is 0.1251
Answer 2
Part a)
i. The standard deviation of the population was provided in the problem, the population was
assumed to follow a normal distribution with mean 10, and standard deviation 10.
At 5% level of significance, the test statistics is calculated as
Z= X

μ
σ
n
=1010
10
100
=0
The two tail rejection region for α =0 . 05 has been indicated in the following figure 1 as |
Z|>1.96 (Ott, and Longnecker, 2015).
Figure 1: Rejection Region at Alpha = 0.05 for Z test
Hence, P (|z|> 0 ) =0. 5 implied that p-value = 1 (p-value > 0.05), which implied that the
null hypothesis failed to get rejected at 5% level of significance.

## End of preview

Want to access all the pages? Upload your documents or become a member.

Related Documents

### Support

#### +1 306 205-2269

Chat with our experts. we are online and ready to help.

©2024 | Zucol Services PVT LTD | All rights reserved.