Question
100%

A machine in the student lounge dispenses coffee. The average cup of coffee is supposed to contain 7.0 ounces. A random sample of seven cups of coffee from this machine show the average content to be 7.2 ounces with a standard deviation of 0.40 ounce. Do you think that the machine has slipped out of adjustment and that the average amount of coffee per cup is different from 7 ounces? Use a 5% level of significance. 

What are we testing in this problem?

single proportion
single mean    

 

(a) What is the level of significance? 
 

State the null and alternate hypotheses.
H0: μ = 7; H1: μ ≠ 7
H0p = 7; H1p < 7    
H0: μ = 7; H1: μ < 7
H0p = 7; H1p ≠ 7
H0: μ = 7; H1: μ > 7
H0p = 7; H1p > 7

(b) What sampling distribution will you use? What assumptions are you making?
The Student's t, since we assume that x has a normal distribution with unknown σ.The Student's t, since n is large with unknown σ.    The standard normal, since we assume that x has a normal distribution with known σ.The standard normal, 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 three decimal places.) 
 

(c) Find (or estimate) the P-value. 
P-value > 0.500
0.250 < P-value < 0.500  
  0.100 < P-value < 0.250
0.050 < P-value < 0.100
0.010 < P-value < 0.050
P-value < 0.010

Sketch the sampling distribution and show the area corresponding to the P-value.
   
   

(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?
At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. 
   At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
At the α = 0.05 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.
There is sufficient evidence at the 0.05 level to conclude that the mean amount of coffee per cup differs from 7 ounces.
There is insufficient evidence at the 0.05 level to conclude that the mean amount of coffee per cup differs from 7 ounces.    
Expert Solution
Check Mark
Blurred answer
Students who’ve seen this question also like:
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
Not helpful? See similar books
MATLAB: An Introduction with Applications
marketing sidebar icon
Your question is solved by a Subject Matter Expert
marketing sidebar icon
Want to see this answer and more?
Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*
*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Get 24/7 homework help!
8+ million solutions
Get access to millions of step-by-step textbook and homework solutions
Support from experts
Send experts your homework questions or start a chat with a tutor
Essay support
Check for plagiarism and create citations in seconds
Solve math equations
Get instant explanations to difficult math equations
Students love us.
Students love us.

Related Statistics Q&A

Find answers to questions asked by students like you.

Q: Jed Home Stores analyzed the value of purchases made on credit card by a random sample of 25 of…

A: Click to see the answer

Q: According to the National Association of builders, the average cost of building a standard warehouse…

A: From the given information, Sample mean (M) = $122.57 Sample size (n) =36 Standard deviation (s) =…

Q: A survey recently reported that the mean national annual expenditure for inpatient and outpatient…

A: Click to see the answer

Q: Consumers know for fact that on valentine’s day, the prices of roses vary with an average of P187. A…

A: Click to see the answer

Q: A manufacturer of chocolate chips would like to know whether its bag filling machine work correctly…

A: Click to see the answer

Q: A local church parish wants to raise money to add to their campus. In a sample from a previous fund…

A: Consider that p1, p2 is the true proportions of people who are contributing in previous fund-raising…

Q: The average American consumes 8.7 liters of alcohol per year. Does the average college student…

A: Given: The average American consumes 8.7 liters (μ0) of alcohol per year. Let n denote the number of…

Q: A professional rock climber claims that he can climb a particular mountain within half an hour. From…

A: It is given that n=25, x=30.5 and s=3.9 To test  H0:μ=30H1:μ&lt;30

Q: A social scientist claims that the average adult watches less than 26 hours of television per week.…

A: The general formula for the test statistic is, z=x¯-μσn

Q: rink dispenser is designed to dispense 250 mL of drink per cup. However, there have been recent…

A: Hypothesis testing is conducted for the parameters of the population like population mean,…

Q: nt is the production manager for Citrus Groves Inc., located just north of Ranikhet, Uttarakhand.…

A: a) sample standard deviation = 30 sample variance = 900 population variance = 900*4142=878.5714…

Q: A phone manufacturer wants to compete in the touch screen phone market. Management understands that…

A: It is given that:n1=120, x1=5×60minutes=300s1=30n2=100x2=8×60 minutes=480s2=55   Since, the sample…

Q: The average time it takes for a person to experience relief from aspirin is 25 minutes. A new…

A: Given that,

Q: The average farm size in the United States is 444 acres. A random sample of 40 farms in Oregon…

A: Given :  μ = 444 σ = 52 x¯ = 430 n = 40 α = 0.05 Hypothesis : H0 : μ = 444 H1 : μ ≠ 444

Q: A consumer advocacy group suspects that a local supermarket’s 10-ounce packages of cheddar cheese…

A: Let Xi : Weight of the ith package, i = lcon.Here , we need to test Ho : u = 10vs Hi : u &lt;…

Q: A local church parish wants to raise money to add to their campus. In a sample from a previous fund…

A: The p-value of the test statistic is 0.143.

Q: A local church parish wants to raise money to add to their campus. In a sample from a previous fund…

A: Click to see the answer

Q: A local church parish wants to raise money to add to their campus. In a sample from a previous fund…

A: Here, in this question we have to find conclusion only with given level of significance α=5% =0.05…

Q: According to the Vivino website, the mean price for a bottle of red wine that scores 4.0 or higher…

A: We have given that  Sample size n=56 , standard deviation s=12 ,sample mean xbar=30.15

Q: The manufacturer of the X-15 steel-belted redial truck tire claims that the mean mileage the tire…

A: Hi! Thank you for the question As per the honour code, We’ll answer the first question since the…

Q: A medical researcher is interested in the prenatal care received by pregnant women in inner cities.…

A: We have given that  Sample size n=20 , sample mean =4  s=1 , 95%confidence.

Q: A medical researcher is interested in the prenatal care received by pregnant women in inner cities.…

A: A sample of 20 randomly selected women with children on the streets of Baltimore and the average…

Q: A particular brand of tires claims that its deluxe tire averages at least 55,000 miles before it…

A: Given :

Q: A soft drink dispenser is designed to dispense 330 ml of drink per cup. However, there have been…

A: The sample mean is 325 and the standard deviation is 20.

Q: The average house price in a country in 2010 was $487,300, according to a real estate organization.…

A: Given information Hypothesized mean µ = $487,300 Sample size (n) = 45 Mean x̅ = $584,760 Standard…

Q: The average house price in a country in 2010 was $487,300, according to a real estate organization.…

A: In order to determine whether the house prices have gone up by over 15% compared with 2010, conduct…

Q: It has been hypothesized that individuals suffering from Alzheimer's Disease may spend less time per…

A: The sample size is 71 and standard deviation is 14.

Q: In the past, patrons of a cinema complex have spent an average of $5.25 for popcorn and other…

A: Click to see the answer

Q: In the past, patrons of a cinema complex have spent an average of $5.25 for popcorn and other…

A: Given Information : In the past, patrons of a cinema complex have spent an average of $5.25 for…

Q: In the past, patrons of a cinema complex have spent an average of $5.25 for popcorn and other…

A: From the provided information, Sample size (n) = 18 Sample mean (x̅) = 4.46 Population standard…

Q: In the past, patrons of a cinema complex have spent an average of $5.25 for popcorn and other…

A: Given Information: In the past, patrons of a cinema complex have spent an average of $5.25 for…

Q: In the past, patrons of a cinema complex have spent an average of $5.25 for popcorn and other…

A: Given Population mean, μ=5.25 Population sd, σ=1.76 Sample size, n=18 Sample mean, X=4.46 α=0.05

Q: In the past, patrons of a cinema complex have spent an average of $5.25 for popcorn and other…

A: Click to see the answer

Q: A marketing researcher wants to estimate the mean amount spent per year​ ($) on a web site by…

A: Assuming the samples are drawn from a normal population. Null Hypothesis(H0):μ= $51Alternate…

Q: The Weather Underground reported that the mean amount of summer rainfall for the northeastern US is…

A: Let µ be the mean amount of summer rainfall for the northeastern US.Claim is that the mean amount of…

Q: A police department claims that the mean life of the tires used on their police cars is no more than…

A: Click to see the answer

Q: A bottling company produces bottles that hold 10 ounces of liquid.​ Periodically, the company gets…

A: Given: μ0=10n=19x¯=9.6s=0.3 The significance level is taken as 0.05.

Q: A marketing researcher wants to estimate the mean amount spent per year ($) on a web site by…

A: Given values, n=100x¯=60s=55

Q: In a recent sample of 89 used cars sales costs, the sample mean was $6,225 with a standard deviation…

A: Given, Sample size = 89 Sample mean = 6225 Sample standard deviation = 3151   Since the population…

Q: A marketing researcher wants to estimate the mean amount spent per year ($) on a web site by…

A: a, Hypothesis: The null and alternate hypotheses are below: H0: μ=52H1: μ≠52 The test statistic is…

Q: A marketing researcher wants to estimate the mean amount spent per year ($) on a web site by…

A: Level of significance, α=0.10

Knowledge Booster
Statistics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
  • MATLAB: An Introduction with Applications
    Statistics
    ISBN:9781119256830
    Author:Amos Gilat
    Publisher:John Wiley & Sons Inc
    Probability and Statistics for Engineering and th...
    Statistics
    ISBN:9781305251809
    Author:Jay L. Devore
    Publisher:Cengage Learning
    Statistics for The Behavioral Sciences (MindTap C...
    Statistics
    ISBN:9781305504912
    Author:Frederick J Gravetter, Larry B. Wallnau
    Publisher:Cengage Learning
  • Elementary Statistics: Picturing the World (7th E...
    Statistics
    ISBN:9780134683416
    Author:Ron Larson, Betsy Farber
    Publisher:PEARSON
    The Basic Practice of Statistics
    Statistics
    ISBN:9781319042578
    Author:David S. Moore, William I. Notz, Michael A. Fligner
    Publisher:W. H. Freeman
    Introduction to the Practice of Statistics
    Statistics
    ISBN:9781319013387
    Author:David S. Moore, George P. McCabe, Bruce A. Craig
    Publisher:W. H. Freeman
  • MATLAB: An Introduction with Applications
    Statistics
    ISBN:9781119256830
    Author:Amos Gilat
    Publisher:John Wiley & Sons Inc
    Probability and Statistics for Engineering and th...
    Statistics
    ISBN:9781305251809
    Author:Jay L. Devore
    Publisher:Cengage Learning
    Statistics for The Behavioral Sciences (MindTap C...
    Statistics
    ISBN:9781305504912
    Author:Frederick J Gravetter, Larry B. Wallnau
    Publisher:Cengage Learning
    Elementary Statistics: Picturing the World (7th E...
    Statistics
    ISBN:9780134683416
    Author:Ron Larson, Betsy Farber
    Publisher:PEARSON
    The Basic Practice of Statistics
    Statistics
    ISBN:9781319042578
    Author:David S. Moore, William I. Notz, Michael A. Fligner
    Publisher:W. H. Freeman
    Introduction to the Practice of Statistics
    Statistics
    ISBN:9781319013387
    Author:David S. Moore, George P. McCabe, Bruce A. Craig
    Publisher:W. H. Freeman