A manufacturer considers his production process to be out of control when defects exceed 3%. In a random sample of 100 items, the defect rate is 4% but the manager claims that this is only a sample fluctuation and production is not really out of control. At the 0.01 level of significance, test the manager's claim.

Answer:

The p-value of the test is of 0.2776 > 0.01, which means that the we accept the null hypothesis, that is, the manager's claim that this is only a sample fluctuation and production is not really out of control.

Step-by-step explanation:

A manufacturer considers his production process to be out of control when defects exceed 3%.

At the null hypothesis, we test if the production process is in control, that is, the defective proportion is of 3% or less. So

[tex]H_0: p \leq 0.03[/tex]

At the alternate hypothesis, we test if the production process is out of control, that is, the defective proportion exceeds 3%. So

[tex]H_1: p > 0.03[/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.

0.03 is tested at the null hypothesis

This means that [tex]\mu = 0.03, \sigma = \sqrt{0.03*0.97}[/tex]

In a random sample of 100 items, the defect rate is 4%.

This means that [tex]n = 100, X = 0.04[/tex]

Value of the test statistic:

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

[tex]z = \frac{0.04 - 0.03}{\frac{\sqrt{0.03*0.97}}{\sqrt{100}}}[/tex]

[tex]z = 0.59[/tex]

P-value of the test

The p-value of the test is the probability of finding a sample proportion above 0.04, which is 1 subtracted by the p-value of z = 0.59.

Looking at the z-table, z = 0.59 has a p-value of 0.7224

1 - 0.7224 = 0.2776

The p-value of the test is of 0.2776 > 0.01, which means that the we accept the null hypothesis, that is, the manager's claim that this is only a sample fluctuation and production is not really out of control.

In ΔDEF, the measure of ∠F=90°, DF = 3, ED = 5, and FE = 4. What is the value of the tangent of ∠E to the nearest hundredth?

PLS HELP 30 POINTS

If the dimensions of the following cylinder are tripled, what factor will the volume change by?



81
27
3
9

Can yah help me with those two question please
:(

1. Adam opened a savings account with
$250. He saves $300 per month.
Mandy opened a savings account
with $750. She saves $200 per
month. How much more will Adam
have in his savings account after 12
months?

Make congruent angles. Write down the ratios.

Freddy earned $7.95 an hour, and last week he worked for 20 hours. About how much money did he earn?

An ice-cream shop uses 1/6 box of waffle cones each day they are open. The shop is open 5 days a week. Which equation shows the amount of a box of waffle cones the ice-cream shop uses in a week?

Evaluate f(x)= 4x-2 when x= -2

2(x + _) = 2x + 10 Using the distributive property, what number would go in the blank in order for the given statement to be correct? ​

The unit rate of fragance a is $ , and the unit rate of fragrance b is $

Helppppppppppppppp meeeeeeeeee

The graph shows two lines, A and B.
6
A
B В
5
4
3
1
0
1 2
3 4 5 6
Part A: How many solutions does the pair of equations for lines A and B have? Explain your answer.
Part B: What is the solution to the equations of lines A and B? Explain your answer.

Simplify using order of operations.​

Identify each triangle based on angles. (Acute, Obtuse or Right)please I don’t understand this

I need the answer fast pls

10 points will give brainliest

320% of 69 is what number?

Please help me answer the question

10 points! If correct you get brainliest.
Which one's apply?

WILL GIVE BRAINLIST






MATH




CONVERT EACH MEASUREMENT

25FT TO YARDS

SHOW STEPS ALL HOW YOU GOT THE ANSWER

10. (05.05 LC)
Determine whether the origin is included in the shaded region and whether the shaded region is above or below the line for the graph of the following inequality: (5 points)
Y
The origin is not included in the shaded region and the shaded area is above the line.
O The origin is not included in the shaded region and the shaded area is below the line.
The origin is included in the shaded region and the shaded area is above the line.
The origin is included in the shaded region and the shaded area is below the line.

Evaluate this expression
4cd

if

C = -4 and d = 3

Please help!!!! I need this to pass my classs

what is the greatest common factor of 20a^2 12a^2 and 8a

Turkey costs $3.38 per pound. If you buy 2.5 pounds of turkey what is the cost of the turkey?

solve the equation
2/3 x (−4/5)

For a year you owe 1600 on a credit card you pay 19% interest a year how much are you paying

Marina starts with $20 in her bank account and she saves $5 each week. Robby has $100 in his bank account, and he saves $2.50 each week. After how many weeks will Macy and Robby have the same amount in their accounts and how much money will that be? Write a system of equations to solve.​

5th grade work helpp

Give m = -1/2 and n = -1/3 which statement is true?