STAT.F/BUS.+ECON.-MYLABSPLUS ACCESS CAR
STAT.F/BUS.+ECON.-MYLABSPLUS ACCESS CAR
13th Edition
ISBN: 9780135411711
Author: MCCLAVE
Publisher: PEARSON
bartleby

Videos

Textbook Question
Chapter 6, Problem 6.106LM

In each of the following instances determine whether you would use a z- or t-statistic (or neither) to form a 95% confidence interval and then look up the appropriate z- or t-value

  1. a. Random sample of size n = 23 from a normal distribution with unknown mean μ and standard deviation σ
  2. b. Random sample of size n − 135 from a normal distribution with unknown mean μ and standard deviation σ
  3. c. Random sample of size n − 10 from a normal distribution with unknown mean  μ and standard deviation s − 5
  4. d. Random sample of size n − 73 from a distribution about which nothing is known
  5. e. Random sample of size n = 12 from a distribution about which nothing is known

(a)

Expert Solution
Check Mark
To determine

To check and find: Whether z-or t-statistic is appropriate for finding the 95% confidence interval and the appropriate z- or t-value for the given information.

Answer to Problem 6.106LM

The t-statistic is appropriate for finding the 95% confidence interval.

The t-value corresponding to the given information is 2.074.

Explanation of Solution

Given info:

The given value is n=23 . The distribution is normal with unknown mean and standard deviation and the level of confidence is 95%.

Calculation:

Conditions for confidence interval of μ when using z-statistic:

(i) Sample size is large. That is, n30 .

(ii) If the population is of any distribution, then z-statistic can be used for confidence interval.

  • If σ is known, then it can be used.
  • If σ is unknown, then the estimate of σ (s) can be used in the confidence interval.

Conditions for confidence interval of μ when using t-statistic:

(i) Sample size is less. That is, n<30 .

(ii) If the population is a normal distribution, then t-statistic can be used for confidence interval.

  • If σ is known, then it can be used.
  • If σ is unknown, then the estimate of σ (s) can be used in the confidence interval.

Here, the sample size is 23, which is less than 30. The mean and standard deviation are unknown.

Hence, the t-statistic can be used to find the confidence interval.

Critical value:

For 95% confidence level:

1α=10.95α=0.05α2=0.052=0.025

Degrees of freedom:

df=n1=231=22

From “Table III of the t distribution in Appendix D”, the critical value is 2.074 for the degrees of freedom of 22.

(b)

Expert Solution
Check Mark
To determine

To check and find: Whether z- or t-statistic is appropriate for finding the 95% confidence interval and the appropriate z- or t-value for the given information.

Answer to Problem 6.106LM

The z-statistic is appropriate for finding the 95% confidence interval.

The z-value corresponding to the given information is 1.96.

Explanation of Solution

Given info:

The value of n=135 . The distribution is normal with unknown mean and standard deviation and the level of confidence is 95%.

Calculation:

Here, the sample size 135, which is greater than 30. Moreover, the mean and standard deviation are unknown. Hence, the population’s standard deviation can be estimated by the sample standard deviation.

Thus, the z-statistic can be used for finding the confidence interval.

Critical value:

For 95% confidence level:

1α=10.95α=0.05α2=0.052=0.025

Hence, the cumulative area to the left is as follows:

Area to the left=1Area to the right=10.025=0.975

From “Table II of the standard normal distribution in Appendix D”, the critical value is 1.96.

(c)

Expert Solution
Check Mark
To determine

To check and find: Whether z- or t-statistic is appropriate for finding the 95% confidence interval and the appropriate z- or t-value for the given information.

Answer to Problem 6.106LM

The t-statistic is appropriate for finding the 95% confidence interval.

The t-value corresponding to the given information is 2.262.

Explanation of Solution

Given info:

The given value are n=10 and s=5 . The distribution is normal with unknown mean and the level of confidence is 95%.

Calculation:

Here, the sample is from a normal distribution with a size is 10, which is less than 30, but the standard deviation is given.

Therefore, the t-statistic can be used for finding the confidence interval.

Critical value:

For 95% confidence level:

1α=10.95α=0.05α2=0.052=0.025

From “Table III of the t distribution in Appendix D”, the critical value is 2.262.

(d)

Expert Solution
Check Mark
To determine

To check and find: Whether z- or t-statistic is appropriate for finding the 95% confidence interval and the appropriate z- or t-value for the given information.

Answer to Problem 6.106LM

The z-statistic is appropriate for finding the 95% confidence interval.

The z-value corresponding to the given information is 1.96.

Explanation of Solution

Given info:

The given value is n=73 and no information is given about distribution.

Calculation:

Here, the distribution is unknown with a sample size of 73, which is larger than 30 and the population’s standard deviation can be estimated by the sample standard deviation.

Therefore, the z-statistic can be used for finding the confidence interval.

Critical value:

For 95% confidence level:

1α=10.95α=0.05α2=0.052=0.025

Hence, the cumulative area to the left is as follows:

Area to the left=1Area to the right=10.025=0.975

From “Table II of the standard normal distribution in Appendix D”, the critical value is 1.96.

(e)

Expert Solution
Check Mark
To determine

To check and find: Whether z- or t-statistic is appropriate for finding the 95% confidence interval and the appropriate z- or t-value for the given information.

Answer to Problem 6.106LM

z or t cannot be used.

Explanation of Solution

Given info:

The given value is n=12 and no information is given about the distribution.

Calculation:

Here, the sample size is 10, which is less than 30, and no information is provided about the distribution.

Also, the above conditions are not satisfied.

Therefore, the z- or t-statistic cannot be used for finding the confidence interval.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Chapter 6 Solutions

STAT.F/BUS.+ECON.-MYLABSPLUS ACCESS CAR

Ch. 6.2 - Will a large-sample confidence interval be valid...Ch. 6.2 - Heart rate variability of police officers. Are...Ch. 6.2 - Tipping points in daily deal transactions? Online...Ch. 6.2 - Corporate sustainability of CPA firms. Corporate...Ch. 6.2 - College dropout study. Refer to the American...Ch. 6.2 - Wear-out of used display panels. Refer to Exercise...Ch. 6.2 - Unethical corporate conduct. How complicit are...Ch. 6.2 - Shopping on Black Friday. The day after...Ch. 6.2 - 401 (k) Participation rates. Named for the section...Ch. 6.2 - Accounting and Machiavellianism. Refer to the...Ch. 6.2 - Facial structure of CEOs. In Psychological Science...Ch. 6.2 - Improving SAT scores. Refer to the Chance (Winter...Ch. 6.2 - The Raid test kitchen. According to scientists,...Ch. 6.3 - Suppose you have selected a random sample of n = 5...Ch. 6.3 - Use the applet Confidence Intervals for a Mean...Ch. 6.3 - Use the applet Confidence Intervals for a Mean...Ch. 6.3 - Explain the differences in the sampling...Ch. 6.3 - Let t0 be a specific value of t. Use Table III in...Ch. 6.3 - The following random sample was selected from a...Ch. 6.3 - The following sample of 16 measurements was...Ch. 6.3 - Lobster trap placement. An observational study of...Ch. 6.3 - Radon exposure in Egyptian tombs. Many ancient...Ch. 6.3 - Do social robots walk or roll? Refer to the...Ch. 6.3 - Hospital length of stay. Health insurers and the...Ch. 6.3 - Repair and replacement costs of water pipes. Refer...Ch. 6.3 - Prob. 6.34ACICh. 6.3 - Oxygen bubbles in molten salt. Molten salt is used...Ch. 6.3 - Performance of stock screeners. In Exercise 2.44...Ch. 6.3 - Minimizing tractor skidding distance. When...Ch. 6.3 - Crude oil biodegradation. Refer to the Journal of...Ch. 6.3 - Largest private companies. IPOsinitial public...Ch. 6.4 - Describe the sampling distribution of p based on...Ch. 6.4 - Use the applet Confidence Intervals for a...Ch. 6.4 - Prob. 6.6AECh. 6.4 - For the binomial sample information summarized in...Ch. 6.4 - A random sample of size n = 121 yielded p=.88. a....Ch. 6.4 - A random sample of size n = 225 yielded p=.46. a....Ch. 6.4 - A random sample of 50 consumers taste-tested a new...Ch. 6.4 - Customer participation in store loyalty card...Ch. 6.4 - Crash risk of using cell phones while driving....Ch. 6.4 - Zillow.com estimates of home values. Zillow.com is...Ch. 6.4 - Do social robots walk or roll? Refer to the...Ch. 6.4 - Is Starbucks coffee overpriced? The Minneapolis...Ch. 6.4 - Nannies who are INA certified. The International...Ch. 6.4 - Prob. 6.51ACICh. 6.4 - Prob. 6.52ACICh. 6.4 - Minority ownership of franchises. According to a...Ch. 6.4 - Study of aircraft bird-strikes. As worldwide air...Ch. 6.4 - Prob. 6.55ACICh. 6.4 - Diamonds sold on the open market. Refer to the...Ch. 6.4 - Are you really being served red snapper? Refer to...Ch. 6.4 - Eye shadow, mascara, and nickel allergies....Ch. 6.4 - Prob. 6.59ACACh. 6.5 - If you wish to estimate a population mean with a...Ch. 6.5 - Suppose you wish to estimate a population mean...Ch. 6.5 - In each case, find the approximate sample size...Ch. 6.5 - The following is a 90% confidence interval for p:...Ch. 6.5 - It costs you 10 to draw a sample of size n = 1 and...Ch. 6.5 - Suppose you wish to estimate the mean of a normal...Ch. 6.5 - If nothing is known about p. .5 can be substituted...Ch. 6.5 - Aluminum cans contaminated by fire. A gigantic...Ch. 6.5 - Accounting and Machiavellianism. Refer to the...Ch. 6.5 - Lobster trap placement. Refer to the Bulletin of...Ch. 6.5 - Evaporation from swimming pools. Refer to the...Ch. 6.5 - Do social robots walk or roll? Refer to the...Ch. 6.5 - Study of aircraft bird-strikes. Refer to the...Ch. 6.5 - Bacteria in bottled water. Is the bottled water...Ch. 6.5 - Shopping on Black Friday. Refer to the...Ch. 6.5 - Monitoring phone calls to a toll-free number. A...Ch. 6.5 - Eye shadow, mascara, and nickel allergies. Refer...Ch. 6.5 - Prob. 6.77ACICh. 6.5 - Is caffeine addictive? Does the caffeine in...Ch. 6.5 - Prob. 6.79ACACh. 6.6 - Calculate the percentage of the population sampled...Ch. 6.6 - Suppose the standard deviation of the population...Ch. 6.6 - Suppose N = 5,000, n = 64, and s = 24. a. Compare...Ch. 6.6 - Suppose N = 10,000, n = 2,000. and s = 50. a....Ch. 6.6 - Prob. 6.84LMCh. 6.6 - Prob. 6.85LMCh. 6.6 - Prob. 6.86LMCh. 6.6 - NFL player survey. Researchers at the University...Ch. 6.6 - Magazine subscriber salaries. Each year, the trade...Ch. 6.6 - Auditing sampling methods. Traditionally. auditors...Ch. 6.6 - Prob. 6.90ACICh. 6.6 - Invoice errors in a billing system In a study of...Ch. 6.6 - Prob. 6.92ACACh. 6.7 - For each of the following combinations of and...Ch. 6.7 - Given the following values of x, s, and n, form a...Ch. 6.7 - Prob. 6.95LMCh. 6.7 - A random sample of n = 6 observations from a...Ch. 6.7 - Oil content of fried sweet potato chips. The...Ch. 6.7 - Corporate sustainability of CPA firms. Refer to...Ch. 6.7 - Facial structure of CEOs. Refer to the...Ch. 6.7 - Radon exposure in Egyptian tombs. Refer to the...Ch. 6.7 - Drug content assessment. Refer to the Analytical...Ch. 6.7 - Jitter in a water power system. Jitter is a term...Ch. 6.7 - Lobster trap placement Refer to the Bulletin of...Ch. 6.7 - Phishing attacks on e-mail accounts. Refer to the...Ch. 6.7 - Is honey a cough remedy? Refer to the Archives of...Ch. 6 - In each of the following instances determine...Ch. 6 - In random Sample of 400 measurements, 227 of the...Ch. 6 - Prob. 6.109LMCh. 6 - Calculate the finite population correction factor...Ch. 6 - Find /22 and (1/2)2 from Table IV, Appendix D, for...Ch. 6 - Latex allergy in health care workers. Health care...Ch. 6 - Prob. 6.113ACBCh. 6 - Products Made in the USA. Refer to Exercise 2.154...Ch. 6 - Prob. 6.115ACBCh. 6 - Lead and copper in drinking water. Periodically,...Ch. 6 - Water pollution testing. The EPA wants to test a...Ch. 6 - Bankruptcy effect on U.S. airfares. Both Delta...Ch. 6 - Prob. 6.119ACBCh. 6 - Motivation of drug dealers. Refer to the Applied...Ch. 6 - Budget lapsing at army hospitals Budget lapsing...Ch. 6 - Size of diamonds sold at retail. Refer to Exercise...Ch. 6 - Prob. 6.123ACICh. 6 - Prob. 6.124ACICh. 6 - Surface roughness of pipe. Refer to the...Ch. 6 - Interviewing candidates for a job. The costs...Ch. 6 - Overbooking policies for major airlines. Airlines...Ch. 6 - Paying for music downloads if you use the...Ch. 6 - Accuracy of price scanners at Walmart. The...Ch. 6 - Contamination of New Jersey wells. Methyl t-butyl...Ch. 6 - Cell phone use by drivers. Studies have shown that...Ch. 6 - Salmonella poisoning from eating an ice cream bar....Ch. 6 - Prob. 6.133ACICh. 6 - Latex allergy in health care workers. Refer to the...Ch. 6 - Prob. 6.135ACACh. 6 - Accountants salary survey. Each year, Management...Ch. 6 - Prob. 6.137ACACh. 6 - A sampling dispute goes to court. Sampling of...Ch. 6 - Prob. 6.139CTC
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
    Hypothesis Testing using Confidence Interval Approach; Author: BUM2413 Applied Statistics UMP;https://www.youtube.com/watch?v=Hq1l3e9pLyY;License: Standard YouTube License, CC-BY
    Hypothesis Testing - Difference of Two Means - Student's -Distribution & Normal Distribution; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=UcZwyzwWU7o;License: Standard Youtube License