Question

The Nero Match Company sells matchboxes that are supposed to have an average of 40 matches...

The Nero Match Company sells matchboxes that are supposed to have an average of 40 matches per box, with σ = 8. A random sample of 96 matchboxes shows the average number of matches per box to be 42.5. Using a 1% level of significance, can you say that the average number of matches per box is more than 40?

What are we testing in this problem?

A.) single mean

B.) single proportion     

(a) What is the level of significance?


State the null and alternate hypotheses.

A.) H0: p = 40; H1:  p > 40

B.) H0: μ = 40; H1:  μ < 40     

C.) H0: μ = 40; H1:  μ ≠ 40

D.) H0: p = 40; H1:  p < 40

E.) H0: μ = 40; H1:  μ > 40

F.) H0: p = 40; H1:  p ≠ 40


(b) What sampling distribution will you use? What assumptions are you making?

A.)The standard normal, since we assume that x has a normal distribution with known σ.

B.)The Student's t, since we assume that x has a normal distribution with known σ.     

C.)The standard normal, since we assume that x has a normal distribution with unknown σ.

D.)The Student's t, since we assume that x has a normal distribution with unknown σ.


What is the value of the sample test statistic? (Round your answer to two decimal places.)


(c) Find (or estimate) the P-value.

A.)P-value > 0.250

B.)0.125 < P-value < 0.250     

C.)0.050 < P-value < 0.125

D.)0.025 < P-value < 0.050

E.)0.005 < P-value < 0.025

F.)P-value < 0.005


(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

A.)At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant

B.)At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.     

C.)At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

D.)At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.


(e) Interpret your conclusion in the context of the application.

A.)There is sufficient evidence at the 0.01 level to conclude that the average number of matches per box is now greater than 40.

B.)There is insufficient evidence at the 0.01 level to conclude that the average number of matches per box is now greater than 40.    

Homework Answers

Answer #1

A.) single mean

a) level of significance=0.01

A.) H0: p = 40; H1:  p > 40

A.)The standard normal, since we assume that x has a normal distribution with known σ.

population mean μ= 40
sample mean 'x̄= 42.500
sample size    n= 96.00
std deviation σ= 8.000
std error ='σx=σ/√n= 0.8165
test stat z = '(x̄-μ)*√n/σ=   3.06

c)

p value        = 0.0011

F.)P-value < 0.005

d)A.)At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant

e)

A.)There is sufficient evidence at the 0.01 level to conclude that the average number of matches per box is now greater than 40.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
The Nero Match Company sells matchboxes that are supposed to have an average of 40 matches...
The Nero Match Company sells matchboxes that are supposed to have an average of 40 matches per box, with σ = 8. A random sample of 96 matchboxes shows the average number of matches per box to be 42.3. Using a 1% level of significance, can you say that the average number of matches per box is more than 40? What are we testing in this problem? single meansingle proportion     (a) What is the level of significance? State the null...
The Nero Match Company sells matchboxes that are supposed to have an average of 40 matches...
The Nero Match Company sells matchboxes that are supposed to have an average of 40 matches per box, with σ = 10. A random sample of 94 matchboxes shows the average number of matches per box to be 42.9. Using a 1% level of significance, can you say that the average number of matches per box is more than 40? What are we testing in this problem? single proportionsingle mean     What is the level of significance? State the null and...
The Nero Match Company sells matchboxes that are supposed to have an average of 40 matches...
The Nero Match Company sells matchboxes that are supposed to have an average of 40 matches per box, with σ = 7. A random sample of 92 matchboxes shows the average number of matches per box to be 42.7. Using a 1% level of significance, can you say that the average number of matches per box is more than 40? What are we testing in this problem? single mean single proportion (a) What is the level of significance? State the...
The Nero Match Company sells matchboxes that are supposed to have an average of 40 matches...
The Nero Match Company sells matchboxes that are supposed to have an average of 40 matches per box, with σ = 11. A random sample of 95 matchboxes shows the average number of matches per box to be 43.0. Using a 1% level of significance, can you say that the average number of matches per box is more than 40? What are we testing in this problem? single meansingle proportion     (a) What is the level of significance? State the null...
The Toylot company makes an electric train with a motor that it claims will draw an...
The Toylot company makes an electric train with a motor that it claims will draw an average of only 0.8 ampere (A) under a normal load. A sample of nine motors was tested, and it was found that the mean current was x = 1.32 A, with a sample standard deviation of s = 0.44 A. Do the data indicate that the Toylot claim of 0.8 A is too low? (Use a 1% level of significance.) What are we testing...
A random sample of 41 adult coyotes in a region of northern Minnesota showed the average...
A random sample of 41 adult coyotes in a region of northern Minnesota showed the average age to be x = 2.09 years, with sample standard deviation s = 0.88 years. However, it is thought that the overall population mean age of coyotes is μ = 1.75. Do the sample data indicate that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years? Use α = 0.01. (a) What is the level of...
The Toylot company makes an electric train with a motor that it claims will draw an...
The Toylot company makes an electric train with a motor that it claims will draw an average of no more than 0.8 amps under a normal load. A sample of nine motors were tested, and it was found that the mean current was x = 1.32 amps, with a sample standard deviation of s = 0.41 amps. Perform a statistical test of the Toylot claim. (Use a 1% level of significance.) A. What are we testing in this problem? Option...
The Toylot company makes an electric train with a motor that it claims will draw an...
The Toylot company makes an electric train with a motor that it claims will draw an average of no more than 0.8 amps under a normal load. A sample of nine motors were tested, and it was found that the mean current was x = 1.32 amps, with a sample standard deviation of s = 0.43 amps. Perform a statistical test of the Toylot claim. (Use a 1% level of significance.) a.) What are we testing in this problem? -single...
Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters...
Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of whole blood. Then x has a distribution that is approximately normal, with population mean of about 14 for healthy adult women. Suppose that a female patient has taken 10 laboratory blood tests during the past year. The HC data sent to the patient's doctor are as follows. 14 17 17 18 15 12 14 18 15 12 (i) Use a calculator with sample...
A random sample of 51 adult coyotes in a region of northern Minnesota showed the average...
A random sample of 51 adult coyotes in a region of northern Minnesota showed the average age to be x = 2.03 years, with sample standard deviation s = 0.80 years. However, it is thought that the overall population mean age of coyotes is μ = 1.75. Do the sample data indicate that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years? Use α = 0.01. (a) What is the level of...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT
Active Questions
  • What are the benefits an organization can enjoy as a result of establishing a strong environment....
    asked 10 minutes ago
  • According to a​ magazine, as of January​ 2018, 9​% of chief executive officers were women. Complete...
    asked 13 minutes ago
  • Solve the initial value problem: 4y′′+3y=0, y(π/2)=2 , y'(π/2)=−1. Give your answer as y=... Use x...
    asked 14 minutes ago
  • Calculate the approximate main-sequence lifetime of a (K0 type) star with a mass of 0.8 mass...
    asked 19 minutes ago
  • Suppose studies indicate that the earth's vegetative mass, or biomass for tropical woodlands, thought to be...
    asked 22 minutes ago
  • Assume the cost of an extended​ 100,000 mile warranty for a particular SUV follows the normal...
    asked 30 minutes ago
  • In response to an attack of 10 missiles, 500 antiballistic missiles are launched. The missile targets...
    asked 32 minutes ago
  • A study indicates that if eight people occupy the elevator, the probability distribution of the total...
    asked 38 minutes ago
  • To resolve an object in an electron microscope, the wavelength of the electrons must be close...
    asked 50 minutes ago
  • Let A = v1 v2 v3 v1 2 8 16 v2 8 0 4 v3 16...
    asked 1 hour ago
  • Earnings per Share, Price-Earnings Ratio, Dividend Yield The following information was taken from the financial statements...
    asked 1 hour ago
  • Required information Many fields of engineering require accurate population estimates. For example, transportation engineers might find...
    asked 1 hour ago