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Kazeer [188]
3 years ago
11

A contract between a manufacturer and a consumer of light bulbs specifies that the mean lifetime of the bulbs must be at least 1

000 hours. As part of the quality assurance program, the manufacturer will institute an inspection program for each day's production of 10,000 units. An ordinary testing procedure is difficult since 1000 hours is over 41 days! Since the lifetime of a bulb decreases as the voltage applied increases, a common procedure is to perform an accelerated lifetime test in which the bulbs are lit using 400 volts (compared to the usual 110 volts). At such a voltage, a 1000-hour bulb is expected to last only 3 hours. This is a well-known procedure, and both sides have agreed that the results from the accelerated test will be a valid indicator of lifetime of the bulb.
The manufacturer will test the hypotheses H0 : µ = 3 versus Ha: µ < 3 at the α = 0.01 significance level with a simple random sample of 100 bulbs.

a. Describe what a Type I error would be in this context.
b. Describe what a Type II error would be in this context.
c. Which error—Type I or Type II—is likely to do more damage to the manufacturer’s relationship with the consumer? Explain.
Mathematics
1 answer:
Alex17521 [72]3 years ago
4 0

Answer:

Follows are the solution to the given points:

Step-by-step explanation:

In point a:

In this sense, describe what type of error I will be.

Type I error: to conclude that perhaps the mean bulb life would be less than three hours when it becomes (at least) 3 hours.

In point b:

Describe throughout this context what the Type II error becomes.

An error of type II: never assuming that its bulbs' mean lifetime is much less than 3 hours. three hours at least

In point c:

What error — type I and type II — would further impact the interaction between the manufacturer and the customer?

A Type II error is probably further problematic because it means that even the buyer will buy bulbs that do not last long.

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If f(x)=logx, explain the transformation that occurs when f(0.25(x-5))+3
nevsk [136]

Answer:

First, let's explain the transformations in a general way:

Vertical shift.

If we have a function f(x), a vertical shift of N units is written as:

g(x) = f(x) + N

This will move the graph of f(x) up or down a distance of N units.

if N is positive, then the shift is upwards

if N is negative, then the shift is downwards.

Horizontal shift.

If we have a function f(x), a horizontal shift of N units is written as:

g(x) = f(x + N)

This will move the graph of f(x) to the right or left a distance of N units.

if N is positive, then the shift is to the left

if N is negative, then the shift is to the right.

Horizontal dilation/contraction.

For a function f(x), an horizontal contraction dilation is written as:

g(x) = f(k*x)

where:

k is called the "scale factor"

If k < 1, then the graph "dilates" horizontally.

if k > 1, then the graph "contracts" horizontally.

Now, in this problem we have:

f(x) = log(x)

And the transformed function is:

g(x) = f(0.25*(x - 5)) + 3

Then, the transformations that take place here are, in order:

Vertical shift of 3 units up:

g(x) = f(x) + 3.

Horizontal shift of 5 units to the right:

g(x) = f(x - 5) + 3

Horizontal dilation of scale factor 0.25

g(x) = f( 0.25*(x - 5)) + 3

replacing f(x) by log(x) we have

g(x) = log(0.25*(x - 5)) + 3.

6 0
2 years ago
Gavin washed 5 windows in 35 minutes. At this rate, how long will it take Gavin to wash 12 windows?
beks73 [17]

Answer: 84 minutes

Step-by-step explanation:

See paper attached. (:

7 0
3 years ago
A unicorn daycare center requires there to be 2 supervisors for every 18 unicorns.
kykrilka [37]

Answer: The number of supervisors are 9 times the number of unicorns.

Step-by-step explanation:

Let the number of supervisors be 'n'.

Let the number of unicorns be 'u'.

According to question, a unicorn daycare center requires there to be 2 supervisors for every 18 unicorns.

So, Mathematically, it is expressed as

\dfrac{n}{u}=\dfrac{2}{18}\\\\\dfrac{n}{u}=\dfrac{1}{9}\\\\9n=u

so, we established the relationship between the number of supervisors and number of unicorns.

Hence, the number of unicorns are 9 times the number of supervisors.

5 0
3 years ago
Read 2 more answers
(c) a farm brings 15 tons of watermelon to market. find a 90% confidence interval for the population mean cash value of this cro
Nina [5.8K]

Answer:

First we need to name some of the variables we are given:n = 38 the sample sizex = 6.88 the sample mean = 1.86 the population standard deviationWe need to find a 90% confidence interval for the mean price per 100 lbs of watermelon: = 1-.90 = .10/2 = .05z(/2) = -1.64-z(/2) = 1.64This can give us a probability expression:P(-1.645 < z < 1.645) = .90The margin of error is calculated with the formula: E = z(/2)(/√n)E = 1.645(1.86/√38) = $.4963(300) = $148.89   Then to calculate the upper and lower limit we add and subtract E from x:lower limit = 6.88 - .4963 = $7.38(300) = $2214upper limit = 6.88 + .4963 = $6.38(300) = $1914Note: We multiply the E, upper and lower limits by 300 because 15 tons is 30000lbs and we need the price per 100 lbs, so we divide 30000/100 and get 300.

Step-by-step explanation:

7 0
1 year ago
Find the measure of C to the nearest degree.
Alisiya [41]

Let the ∠C be : θ

From the figure, We can see that the Side which is opposite to angle θ is measuring 7 units

Also, We can notice that Hypotenuse is 11 units

As we are dealing with opposite and hypotenuse, we can clearly use Sinθ to find out the angle θ

We know that :

\bigstar \ \ \boxed{\sf{Sin\theta = \dfrac{Opposite \ Side}{Hypotenuse}}}

\implies \sf{Sin\theta = \dfrac{7}{11}}

\implies \sf{\theta = Sin^{-1}\bigg(\dfrac{7}{11}\bigg)}

\implies \sf{\theta = 39.52^{\circ}}

<u>Answer</u> : The measure of ∠C to the nearest degree is 38°

3 0
3 years ago
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