Mathematics, 22.07.2021 19:20 lesliemar

A machine in a factory must be repaired if it produces more than 10% defectives in production. A random sample of 100 items from a day's production contains 15 defectives, and the foreman says that the machine must be repaired. Statistically, does the sample evidence support his decision to repair at the 0.01 significance level? Conduct a test by using both the critical region method and the p-value method.

Answers: 3

Show answers

Answers

From the test the person wants, and the sample data, we build the test hypothesis, find the test statistic, and use this to reach a conclusion both using the critical value and the p-value.

Doing this, the conclusions are:

The test statistic is z = 1.67 < z_c

, meaning that there is not enough evidence to conclude that the proportion of defectives is above 10%, that is, it does not support his decision to repair at the 0.01 significance level.The p-value of the test is 0.0475 > 0.01, meaning that there is not enough evidence to conclude that the proportion of defectives is above 10%, that is, it does not support his decision to repair at the 0.01 significance level.

---------------------------------------------------------

Hypothesis:

A machine in a factory must be repaired if it produces more than 10% defectives in production.

At the null hypothesis, we test if it does not have to be repaired, that is, the proportion is of at most 10%. So

$H_0: p \leq 0.1$

At the alternative hypothesis, we test if it does have to be repaired, that is, the proportion is greater than 10%. So

H_1: p 0.1

------------------------------------------------------

Decision rule:

0.01 significance level, using a left-tailed test(testing if the mean is more than a value), which means that:

The critical value is Z with a p-value of 1 - 0.01 = 0.99, so Z_c = 2.327

. If the test statistic z is less than this, there is not enough evidence to reject the null hypothesis, that the proportion is of at most 10%, otherwise, there is.The p-value is the probability of finding a sample proportion above the one found. If it is more than 0.01, there is not enough evidence to reject the null hypothesis, otherwise, there is.

----------------------------------------------------------

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, is the value tested at the null hypothesis, is the standard deviation and n is the size of the sample.

0.1 is tested at the null hypothesis:

This means that $\mu = 0.1, \sigma = \sqrt{0.1*0.9}$

A random sample of 100 items from a day's production contains 15 defectives.

This means that $n = 100, X = \frac{15}{100} = 0.15$

Value of the test-statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{0.15 - 0.1}{\frac{\sqrt{0.1*0.9}}{\sqrt{100}}}$

z = 1.67

----------------------------------------------

Decision: Critical region

The test statistic is z = 1.67 < z_c , meaning that there is not enough evidence to conclude that the proportion of defectives is above 10%, that is, it does not support his decision to repair at the 0.01 significance level.

Decision: p-value

The p-value of the test is the probability of finding a sample proportion above 0.15, which is 1 subtracted by the p-value of z = 1.67.

Looking at the z-table, z = 1.67 has a p-value of 0.9525.

1 - 0.9525 = 0.0475.

The p-value of the test is 0.0475 > 0.01, meaning that there is not enough evidence to conclude that the proportion of defectives is above 10%, that is, it does not support his decision to repair at the 0.01 significance level.

A similar problem is found at

Answer from: Quest

30 people weigh 160 pounds or more

According to the histogram above how many people weigh 160 pounds or more?

Answer from: Quest

the car was traveling 40 mph before it started skidding. ( 2 points ) 17. was the driver were her brakes working at 75% efficiency or better? ( 2 points ) yes 29.

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 22:00

You're locked out of your house. the only open window is on the second floor, 25 feet above the ground. there are bushes along the edge of the house, so you will need to place the ladder 10 feet from the house. what length ladder do you need to reach the window?

Answers: 3

Answer

Mathematics, 21.06.2019 22:30

One number is 4 less than 3 times a second number. if 3 more than two times the first number is decreased by 2 times the second number, the result is 11. use the substitution method. what is the first number?

Answers: 1

Answer

Mathematics, 21.06.2019 23:00

The ratio of the perimeters of two similar triangles is 4: 3. what are the areas of these triangles if the sum of their areas is 130cm2?

Answers: 3

Answer

Mathematics, 21.06.2019 23:00

At river bank, checking account customers earn 0.75% interest a month on their account balances, pay no service fees for writing checks, and pay a monthly $2.00 financial charge. calculate the income earned in one month on the checking account for a customer with an account balance of $1,000. a. $4.25 b. $5.50 c. $6.75 d. $7.25 checking account earnings at baker’s bank are expressed by the equation: i = -0.09x + 10.2. while the earnings at elite bank are modeled by: i = -0.02x + 7.5. in both cases, x is the number of checks written. at what number of checks will elite bank start generating more checking account income than baker's bank? a. 12 b. 25 c. 39 d. 42 emilio’s checking account had a balance of 728.32 at the beginning of the week. he wrote checks for the following amounts throughout the week: $99.48, $33.50, $18.23, and $72.05. he also deposited his paycheck in the amount of $1,109.90. what is his account balance at the end of the week? a. $1,192.35 b. $1,222.86 c. $1,540.52 d. $1,614.96

Answers: 1

Answer

You know the right answer?

A machine in a factory must be repaired if it produces more than 10% defectives in production. A ran...

Questions

Mathematics, 28.06.2019 18:30

Madeline works as a part time job at parkland hospital for $20 per hour. she worked for 10 hours last week and must pay 10% in taxes. what is madeline...

Mathematics, 28.06.2019 18:30

What is the inequality of p-1> 3...

Mathematics, 28.06.2019 18:30

10^4×4^10/4^5 equals to what? a)10^4×4^5 b)4^9 c)40^9 d)10^4×4^15...

Mathematics, 28.06.2019 18:30