A random sample of 8 cigarettes of a certain brand has an average nicotine content of 4.2 milligrams and a standard deviation of 1.4 milligrams. Is this in line with the manufacturer’s claim that the average nicotine content does not exceed 3.5 mg? Use a 0.01 level of significance and assume the distribution of nicotine contents to be normal.

Answer:

0.0793 > 0.01, which means that we have a result in line with the manufacturer's claim.

Step-by-step explanation:

Manufacturer’s claim that the average nicotine content does not exceed 3.5 mg

This means that the null hypothesis is given by:

[tex]H_{0}: \mu = 3.5[/tex]

And the alternate hypothesis is:

[tex]H_{a}: \mu > 3.5[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

3.5 is tested at the null hypothesis

This means that [tex]\mu = 3.5[/tex]

A random sample of 8 cigarettes of a certain brand has an average nicotine content of 4.2 milligrams and a standard deviation of 1.4 milligrams.

This means that [tex]n = 8, X = 4.2, \sigma = 1.4[/tex]

Value of the z-statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{4.2 - 3.5}{\frac{1.4}{\sqrt{8}}}[/tex]

[tex]z = 1.41[/tex]

Pvalue of the test:

We are testing if the mean is higher than 3.5.

The sample mean found is of 4.2, and we have to find the probability of finding a sample mean at least as large as this, which is 1 subtracted by the pvalue of z = 1.41.

z = 1.41 has a pvalue of 0.9207

1 - 0.9207 = 0.0793

0.0793 > 0.01, which means that we have a result in line with the manufacturer's claim.

i get a 25% discount (means decrease) at macys store. if i find a dress i like for $80, how much will i have to pay for it?​

This net could be folded to form a This figure will have v faces vertices. edges, and a​

Determine the minimum sample size required when you want to be99 ​% confident that the sample mean is within one unit of the population mean and o=14.8 . Assume the population is normally distributed.
A confidence level 99%
requires a sample size of

1. What is the solution of n^2-49=0?
a. -7
b.7
c.≠7
d. no solution

2. What is the solution of x^2+64=0?
a.-5
b.8
c.≠8
d.no solution

3. What is the length of a square with an area of 144x^2
a.12
b.12x
c.≠4in
d.no solution

4. What is the value of b in the triangle?
a.-4in
b.4in
c.≠4in
d.no solution

5. What is the value of z so that -9 and 9 are both solutions of x^2+z=103

Identify the coordinates for point C Type your answer in the form (#.#), without spaces.​

To get ready for the new season Jayden bought new basketball sneakers. Jayden paid $96.12 after paying the 8% tax. How much were the sneakers before including the tax?
Show your work here:

One day last summer, Tommy decided to take a drive into the countryside.

After a few hours' drive he arrived at a farm stand. Tommy was so excited by the sight of all those fresh fruits and veggies, that he tripped getting out of his MG and knocked over a huge basket of eggs. And of course they all broke!

He asked the farmer how many eggs were in the basket because he obviously wanted to compensate her for them. She said she didn't know exactly.

"But I do know,' she said, "that this morning I decided the eggs would be easier to sell if they weren't in a big basket but if they were in little paper bags.

"So when I took all my eggs and placed two in each bag I had one left over. I didn't like that so I took the eggs and I put three in each bag. And when I did that, I also had one left over.
"When I put four in each bag, I had one left over. When I put five in a bag or six in a bag, I had one left over. And when I put seven in a bag, I had none left over."


So here's the question: what's the smallest number of eggs that Tommy should have to pay for?

Emma's dad and her Uncle Pete are trying to recreate their dad's famous dipping sauce for an upcoming family reunion. They remember thinking the sauce was too spicy when they were kids, but they can't remember exactly how much spicy chipotle sauce and tangy mayonnaise to mix now. Emma's dad uses 8 tablespoons of chipotle sauce and 12 tablespoons of mayonnaise. Uncle Pete uses 6 tablespoons of chipotle sauce and 10 tablespoons of mayonnaise. Who makes a spicier sauce?

NO LINKS PLEASE!!!!!!!

A class sets up 40 chairs. There 8 chairs in each row. How many rows of chairs are there?

Amir can run 15 kilometers in one hour. How many kilometers can Amir run per minute? There are 60 minutes in 1 hour.

graph the circle which is centered at (-1 -3) and which has the point (-7 -3) on it

please answer the attached question.

if a number × is increased by 11,the result is 35.What is the number?​

Check the pic please
I also want the steps pleaseee

What is the value (Shown in the picture) of f(81)?

A full bottle holds 1/4gallon of juice, If of3/5
the juice has beenpored how much
juice is left in the bottle?

I need help with slopes!

what is 4649+3383473

6C + 47M=893.50
25C + 22M=527.86

1. Determine P(green) and P(orange for the spinner. Write the probabilities as fractions, decimals and percents.

I need help with this math assignment ASAP

. A certain rectangular prism is
4 inches long, 2 inches wide, and
3 inches high. Sketch the figure
and find its volume.

What two numbers add up to 4 and multiply to -60

Please help .. would be appreciated

Triangle ABC is similar to triangle DEF. how long is EF?
A) 4
B) 10
C) 14
D) 12

What is 6 +0.2 + 0.09 written in standard form? A 0.629 B 6.029 C 6.209 D 6.29
​

To the nearest dollar, how much did the business initially invest in 1991
A. $4,637
B. $4,631
C. $3,450
D. $3,455

Solve each equation.

4) x2+21=102 5) x2-6=-2
6) 80= x2-64x3+25=150 8) x2-14=155 9) x3+5=221
BRAINLIEST

Write 186% as a mixed number in simplest form

200000*900000= what HELP PLEASE
I'll mark brainliest