A manufacturer must test that his bolts are 4.00 cm long when they come off the assembly line. He must recalibrate his machines if the bolts are too long or too short. After sampling 196 randomly selected bolts off the assembly line, he calculates the sample mean to be 4.14 cm. He knows that the population standard deviation is 0.83 cm. Assuming a level of significance of 0.05, is there sufficient evidence to show that the manufacturer needs to recalibrate the machines? State the null and alternative hypotheses for the test.

Answer:

The null hypothesis is [tex]H_o: \mu = 4[/tex].

The alternate hypothesis is [tex]H_a: \mu \neq 4[/tex]

The pvalue of the test is 0.0182 < 0.05, which means that there is sufficient evidence to show that the manufacturer needs to recalibrate the machines.

Step-by-step explanation:

A manufacturer must test that his bolts are 4.00 cm long when they come off the assembly line.

This means that the null hypothesis is that they are 4.00 cm long, that is:

[tex]H_o: \mu = 4[/tex]

At the alternate hypothesis we test if it is different. So

[tex]H_a: \mu \neq 4[/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.

4 is tested at the null hypothesis:

This means that [tex]\mu = 4[/tex]

After sampling 196 randomly selected bolts off the assembly line, he calculates the sample mean to be 4.14 cm.

This means that [tex]n = 196, X = 4.14[/tex]

He knows that the population standard deviation is 0.83 cm.

This means that [tex]\sigma = 0.83[/tex]

Value of the test statistic:

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

[tex]z = \frac{4.14 - 4}{\frac{0.83}{\sqrt{196}}}[/tex]

[tex]z = 2.36[/tex]

Pvalue of the test and decision:

The pvalue of the test is the probability that the sample mean is different by at least 4.14 - 4 = 0.14 from the target value, which is P(|z| > 2.36), which is 2 multiplied by the pvalue of z = -2.36.

Looking at the z-table, z = -2.36 has a pvalue of 0.0091

2*0.0091 = 0.0182

The pvalue of the test is 0.0182 < 0.05, which means that there is sufficient evidence to show that the manufacturer needs to recalibrate the machines.

Which list shows the numbers NOT in order from greatest to least

A right triangle has a height of 18 inches and a base of 12 inches. Find the area of the triangle in square inches. Enter only the number. The solution is​

Find the area of the following parallelogram:​

Review
Francisco v
O GRAPHING. FUNCTIONS, AND LINEAR SYSTEMS
Solving a word problem involving a sum and another basic...
A textbook store sold a combined total of 432 physics and biology textbooks in a week. The number of physics textbooks sold was 60 more than the number of
biology textbooks sold. How many textbooks of each type were sold?

23. Find the value of B.
24.Find the value of x.

look at pic 10 pts will mark brainilest

What is the value of x?

What is the solution to the to system equations in the graph?

WHAT IS THE ANSWER PLSS

please help quick please

Parka's and more was having a 10% off sale. Find the amount saved on a rain jacket that regularly costs $74.00.

Plssss help what is x

solve 4z+6v=124z+6v=12 for vv

Comcast Corporation is the largest cable television company, the second largest Internet service provider, and the fourth largest telephone service provider in the United States. Generally known for quality and reliable service, the company periodically experiences unexpected service interruptions. On January 14, 2009, such an interruption occurred for the Comcast customers living in southwest Florida. When customers called the Comcast office, a recorded message told them that the company was aware of the service outage and that it was anticipated that service would be restored in two hours. Assume that two hours is the mean time to do the repair and that the repair time has an exponential probability distribution.
a. What is the probability that the cable service will be repaired in one hour or less?
b. What is the probability that the repair will take between one hour and two hours?
c. For a customer who calls the Comcast office at 1:00 P.M., what is the probability that the cable service will not be repaired by 5:00 P.M.?

runs 12 miles in 90 minutes. How many minutes does he take per mile?

​

Brianna measures the temperature of two chemical samples. If the first sample measures -8 degrees Celsius and the second sample measures 24 degrees Celsius, what is the average temperature of the two samples? *

Pls help me if I cabbnnnnsbdhdhdjdjxjkxx

The number of guppies that a fish tank can safely hold depends on its volume. A fish tank should have a volume of 576 cubic inches to safely hold 3 guppies. How many guppies can a fish tank that is 24 inches long, 12 inches wide, and 16 inches high safely hold? It can safely hold ___ guppies.

Ethan purchased a new cell phone for $75.00. The costs of the phone is included in his first month's bill. His cell phone plan charges $0.06 for each minute used.

if Ethan has $90.00 to spend on his first month's bill, what is the maximum number of minutes he can use?

A. 80 minutes
B. 250 minutes
C. 1,250 minutes
D. 1,500 minutes​

In 2001, gas cost $1.85 per gallon. In 2008, the price was
220% higher than in 2001.
What was the cost of gas per gallon in 2008?

Please help!!!!!!!!!!!! Bbb

28 divided by 6 is?? I’m in the 7th grade helping my little sis out can remeber this stuff

Find the third side in simplest radical form:
28
45

BC is included between?

Find the value of x. help please if you understand

The probability that Joanne has eggs for breakfast and goes to school by car is 0.4. The probability that she goes to school by car on any day is 0.5. What is the probability that Joanne has had eggs for breakfast if she went to school by car?

A) .1
B) .2
C) .4
D) .5
E) .8

Write the following expression in standard form by expanding and collecting like
terms.

(6g- 27) = 3

WILL MARK BRIANLIST IF GOTTEN RIGHT!!!

How do I do number 2 and 4 please help

Can you help me worth 16 points if your help me all the way