# A random sample of 42 mechanic

A random sample of 42 mechanical gears has been collected, andthe measurements ofGear-Diameter (mm) are found below:130 131 132 130.5 130 130.2 130.7 130 131.2 133130 130 131 132 133 133 132 131 312.5 131.5131.2 132.5 130.2 129.5 131 130 130.2 131.5 131.4 131.6130.6 130.5 131.1 130 13 130 131 130 130 132131.2 132(a) Construct a 94% two-bounds confidence interval on thediameter.(b) Construct a 94% lower confidence bound on the diameter.

A random sample of 42 mechanical gears is given below

130 131 132 130.5 130 130.2 130.7 130 131.2 133130 130 131 132 133 133 132 131 312.5 131.5131.2 132.5 130.2 129.5 131 130 130.2 131.5 131.4 131.6130.6 130.5 131.1 130 13 130 131 130 130 132131.2 132

[ Note that one observation is ” 13 ” which looks likeincorrect entry , but due to no evidence we will continuecalculation with considering “13” as correct entry ]

Here n = 42 ( sample size )

Now we will calculate sample mean and sample variance s2

=

= ( 130 +131 +132 +130.5 +130 + …….. + 130 +132+131.2 +132 ) /42

= 5565.1 / 42

= 132.5024

And

s2 =

= { (130-132.5024)2 +(131-132.5024)2+(132-132.5024)2 +……. + (131.2-132.5024)2+(132-132.5024)2 } / (42-1)

s2 = 46806.77 / 41

s2 = 1141.629

Thus sample standard deviation s = = 33.78799

So we have

= 132.5024     ,     s = 33.78799

(a) Construct a 94% two-bounds confidence interval on thediameter.

94% two-bounds confidence interval CI is given by

CI = {   * , * }

where is t-distributed with n-1 = 42-1 = 41 degree of freedom (DF) and= 0.06 { for 94% confidence }

Now at = 0.06 with DF = 41 , can be obtained from statistical book orfrom any software like R/Excel

From R

>qt(1-0.06/2,df=41)            [1] 1.934283

Hence = 1.934283

Thus

CI = {   * , + * }

CI = {   132.5024 – 1.934283 * , 132.5024 + 1.934283 * }

CI = { 122.4178 , 142.587}                        [ after calculation ]

Hence 94% two-bounds confidence interval on the diameteris { 122.4178 , 142.587}

b) Construct a 94% lower confidence bounds on the diameter.

94% lower confidence bound LB is given by

LB =    *

Now is t-distributed at = 0.06 with DF = 41

Calculation from R , since in can’t find accurate value at df=41 and = 0.06 in statistical book

From R

> qt(1-0.06,df=41)[1] 1.587865

Hence   = 1.587865

Thus

LB = *

LB = 132.5024 – 1.587865 *

LB = {   132.5024 – 8.278494

LB = 124.2239

{ CI = { 124.2239 , Inf } or > 124.2239 }

Hence 94% lower confidence bounds on the diameter is LB= 124.2239

##### "Our Prices Start at \$11.99. As Our First Client, Use Coupon Code GET15 to claim 15% Discount This Month!!"
Calculate the price
Pages (550 words)
\$0.00
*Price with a welcome 15% discount applied.
Pro tip: If you want to save more money and pay the lowest price, you need to set a more extended deadline.
We know how difficult it is to be a student these days. That's why our prices are one of the most affordable on the market, and there are no hidden fees.

Instead, we offer bonuses, discounts, and free services to make your experience outstanding.
How it works
Receive a 100% original paper that will pass Turnitin from a top essay writing service
step 1
Fill out the order form and provide paper details. You can even attach screenshots or add additional instructions later. If something is not clear or missing, the writer will contact you for clarification.
Pro service tips
How to get the most out of your experience with brilliantassignmenthelp.com
One writer throughout the entire course
If you like the writer, you can hire them again. Just copy & paste their ID on the order form ("Preferred Writer's ID" field). This way, your vocabulary will be uniform, and the writer will be aware of your needs.
The same paper from different writers
You can order essay or any other work from two different writers to choose the best one or give another version to a friend. This can be done through the add-on "Same paper from another writer."
Copy of sources used by the writer
Our college essay writers work with ScienceDirect and other databases. They can send you articles or materials used in PDF or through screenshots. Just tick the "Copy of sources" field on the order form.
Testimonials
See why 20k+ students have chosen us as their sole writing assistance provider
Check out the latest reviews and opinions submitted by real customers worldwide and make an informed decision.
11,595
Customer reviews in total
96%
Current satisfaction rate
3 pages
Average paper length
37%
Customers referred by a friend
Use a coupon FIRST15 and enjoy expert help with any task at the most affordable price.
Claim my 15% OFF Order in Chat