Videos
(a)
To graph: A diagram with the use of confidence interval applet.
(a)
Explanation of Solution
Calculation: To construct confidence inetrvals, use confidence interval applet. The following steps are provided below:
Step 1: Go to the “Confidence interval applets” in the website. The screenshot is
shown below:
Step 2: Specify confidence interval as “80” and specify the
Step 3: Click on the “Sample 25” to generate the sample. The screenshot is shown below:
Graph: The obtained output is shown below:
From the above srceenshot, intervals that contain the true
Interpretation: From the above output, out of a total 25, 21 intervals contain the true mean and the proportion of the interval that contains true mean is 84%.
(b)
To find: The confidence interval with 50 SRSs.
(b)
Answer to Problem 5UYK
Solution: The confidence interval with 50 SRSs is shown below:
Explanation of Solution
Calculation: To construct confidence intervals, use confidence interval applet. The following steps are provided below:
Step 1: Go to the “Confidence interval applets” in the website. The screenshot is shown below:
Step 2: Specify confidence interval as “80” and specify the sample size as “20.” The screenshot is shown below:
Step 3: Click twice on the “Sample 25” to generate the sample. The screenshot is shown below:
The obtained output is shown below:
From the above sceenshort, intervals that contain the true mean
Interpretation: The above figure indicates the hit 35, total 50, and percent hit 70%. Thirty-five out of 50 intervals contain the true mean and the proportion of the interval that contains the true mean is 70%.
To find: The confidence interval with 100 SRSs.
Answer to Problem 5UYK
Solution: The confidence interval with 100 SRSs is shown below:
Explanation of Solution
Calculation: To construct confidence inetrvals, use confidence interval applet. The following steps are provided below:
Step 1: Go to the “Confidence interval applets” in the website. The screenshot is shown below:
Step 2: Specify confidence interval as “80” and specify the sample size as “20.” The screenshot is shown below:
Step 3: Click four times on the “Sample 25” to generate the sample. The screenshot is shown below:
The obtained output is shown below:
From the above sceenshort, intervals that contain the true mean
Interpretation: The above figure indicates the hit 75, total 100, and percent hit 75%. Seventy-five out of 100 intervals contain the true mean and the proportion of the interval that contains the true mean is 75%.
To find: The confidence interval with 200 SRSs.
Answer to Problem 5UYK
Solution: The confidence interval with 200 SRSs is shown below:
Explanation of Solution
Calculation: To construct confidence inetrvals, use confidence interval applet. The following steps are provided below:
Step 1: Go to the “Confidence interval applets” in the website. The screenshot is shown below:
Step 2: Specify confidence interval as “80” and specify the sample size as “20.” The screenshot is shown below:
Step 3: Click eight times on the “Sample 25” to generate the sample. The screenshot is shown below:
The obtained output is shown below:
From the above sceenshort, intervals that contain the true mean
Interpretation: The above figure indicates the hit 157, total 200, and percent hit 79%. One hundred and fifty-seven out of 200 intervals contain the true mean and the proportion of the interval that contains the true mean is 79%.
To find: The confidence interval with 300 SRSs.
Answer to Problem 5UYK
Solution: The confidence interval with 300 SRSs is shown below:
Explanation of Solution
Calculation: To construct confidence inetrvals, use confidence interval applet. The following steps are provided below:
Step 1: Go to the “Confidence interval applets” in the website. The screenshot is shown below:
Step 2: Specify confidence interval as “80” and specify the sample size as “20.” The screenshot is shown below:
Step 3: Click 12 times on the “Sample 25” to generate the sample. The screenshot is shown below:
The obtained output is shown below:
From the above sceenshort, intervals that contain the true mean
Interpretation: The above figure indicates the hit 232, total 300, and percent hit 77%. Two hundred and thirty-two out of 300 intervals contain the true mean and the proportion of the interval that contains the true mean is 77%.
To find: The confidence interval with 400 SRSs.
Answer to Problem 5UYK
Solution: The confidence interval with 400 SRSs is shown below:
Explanation of Solution
Calculation: To construct confidence inetrvals, use confidence interval applet. The following steps are provided below:
Step 1: Go to the “Confidence interval applets” in the website. The screenshot is shown below:
Step 2: Specify confidence interval as “80” and specify the sample size as “20.” The screenshot is shown below:
Step 3: Click 16 times on the “Sample 25” to generate the sample. The screenshot is shown below:
The obtained output is shown below:
From the above sceenshort, intervals that contain the true mean
Interpretation: The above figure indicates the hit 315, total 400, and percent hit 79%. Three hundred and fifteen out of 400 intervals contain the true mean and the proportion of the interval that contains the true mean is 79%.
To find: The confidence interval with 500 SRSs.
Answer to Problem 5UYK
Solution: The confidence interval with 500 SRSs is shown below:
Explanation of Solution
Calculation: To construct confidence inetrvals, use confidence interval applet. The following steps are provided below:
Step 1: Go to the “Confidence interval applets” in the website. The screenshot is shown below:
Step 2: Specify confidence interval as “80” and specify the sample size as “20.” The screenshot is shown below:
Step 3: Click 20 on the “Sample 25” to generate the sample. The screenshot is shown below:
The obtained output is shown below:
From the above sceenshort, intervals that contain the true mean
Interpretation: The above figure indicates the hit 397, total 500, and percent hit 79%. Three hundred and ninety-seven out of 500 intervals contain the true mean and the proportion of the interval that contains the true mean is 79%. From the pattern in the above seven cases, the proportion hit approaches near by 80% as the number of sample increases. Thus, one should expect that the percent capture to get closer to the confidence interval level is 80% as the number of samples increases.
Want to see more full solutions like this?
Chapter 6 Solutions
Introduction to the Practice of Statistics
- Suppose the Internal Revenue Service reported that the mean tax refund for the year 2022 was $3401. Assume the standard deviation is $82.5 and that the amounts refunded follow a normal probability distribution. Solve the following three parts? (For the answer to question 14, 15, and 16, start with making a bell curve. Identify on the bell curve where is mean, X, and area(s) to be determined. 1.What percent of the refunds are more than $3,500? 2. What percent of the refunds are more than $3500 but less than $3579? 3. What percent of the refunds are more than $3325 but less than $3579?arrow_forwardA normal distribution has a mean of 50 and a standard deviation of 4. Solve the following three parts? 1. Compute the probability of a value between 44.0 and 55.0. (The question requires finding probability value between 44 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 44, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the answer of the second part.) 2. Compute the probability of a value greater than 55.0. Use the same formula, x=55 and subtract the answer from 1. 3. Compute the probability of a value between 52.0 and 55.0. (The question requires finding probability value between 52 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 52, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the…arrow_forwardIf a uniform distribution is defined over the interval from 6 to 10, then answer the followings: What is the mean of this uniform distribution? Show that the probability of any value between 6 and 10 is equal to 1.0 Find the probability of a value more than 7. Find the probability of a value between 7 and 9. The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $20 and $30 per share. What is the probability that the stock price will be: More than $27? Less than or equal to $24? The April rainfall in Flagstaff, Arizona, follows a uniform distribution between 0.5 and 3.00 inches. What is the mean amount of rainfall for the month? What is the probability of less than an inch of rain for the month? What is the probability of exactly 1.00 inch of rain? What is the probability of more than 1.50 inches of rain for the month? The best way to solve this problem is begin by a step by step creating a chart. Clearly mark the range, identifying the…arrow_forward
- Client 1 Weight before diet (pounds) Weight after diet (pounds) 128 120 2 131 123 3 140 141 4 178 170 5 121 118 6 136 136 7 118 121 8 136 127arrow_forwardClient 1 Weight before diet (pounds) Weight after diet (pounds) 128 120 2 131 123 3 140 141 4 178 170 5 121 118 6 136 136 7 118 121 8 136 127 a) Determine the mean change in patient weight from before to after the diet (after – before). What is the 95% confidence interval of this mean difference?arrow_forwardIn order to find probability, you can use this formula in Microsoft Excel: The best way to understand and solve these problems is by first drawing a bell curve and marking key points such as x, the mean, and the areas of interest. Once marked on the bell curve, figure out what calculations are needed to find the area of interest. =NORM.DIST(x, Mean, Standard Dev., TRUE). When the question mentions “greater than” you may have to subtract your answer from 1. When the question mentions “between (two values)”, you need to do separate calculation for both values and then subtract their results to get the answer. 1. Compute the probability of a value between 44.0 and 55.0. (The question requires finding probability value between 44 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 44, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the…arrow_forward
- If a uniform distribution is defined over the interval from 6 to 10, then answer the followings: What is the mean of this uniform distribution? Show that the probability of any value between 6 and 10 is equal to 1.0 Find the probability of a value more than 7. Find the probability of a value between 7 and 9. The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $20 and $30 per share. What is the probability that the stock price will be: More than $27? Less than or equal to $24? The April rainfall in Flagstaff, Arizona, follows a uniform distribution between 0.5 and 3.00 inches. What is the mean amount of rainfall for the month? What is the probability of less than an inch of rain for the month? What is the probability of exactly 1.00 inch of rain? What is the probability of more than 1.50 inches of rain for the month? The best way to solve this problem is begin by creating a chart. Clearly mark the range, identifying the lower and upper…arrow_forwardProblem 1: The mean hourly pay of an American Airlines flight attendant is normally distributed with a mean of 40 per hour and a standard deviation of 3.00 per hour. What is the probability that the hourly pay of a randomly selected flight attendant is: Between the mean and $45 per hour? More than $45 per hour? Less than $32 per hour? Problem 2: The mean of a normal probability distribution is 400 pounds. The standard deviation is 10 pounds. What is the area between 415 pounds and the mean of 400 pounds? What is the area between the mean and 395 pounds? What is the probability of randomly selecting a value less than 395 pounds? Problem 3: In New York State, the mean salary for high school teachers in 2022 was 81,410 with a standard deviation of 9,500. Only Alaska’s mean salary was higher. Assume New York’s state salaries follow a normal distribution. What percent of New York State high school teachers earn between 70,000 and 75,000? What percent of New York State high school…arrow_forwardPls help asaparrow_forward
- Solve the following LP problem using the Extreme Point Theorem: Subject to: Maximize Z-6+4y 2+y≤8 2x + y ≤10 2,y20 Solve it using the graphical method. Guidelines for preparation for the teacher's questions: Understand the basics of Linear Programming (LP) 1. Know how to formulate an LP model. 2. Be able to identify decision variables, objective functions, and constraints. Be comfortable with graphical solutions 3. Know how to plot feasible regions and find extreme points. 4. Understand how constraints affect the solution space. Understand the Extreme Point Theorem 5. Know why solutions always occur at extreme points. 6. Be able to explain how optimization changes with different constraints. Think about real-world implications 7. Consider how removing or modifying constraints affects the solution. 8. Be prepared to explain why LP problems are used in business, economics, and operations research.arrow_forwardged the variance for group 1) Different groups of male stalk-eyed flies were raised on different diets: a high nutrient corn diet vs. a low nutrient cotton wool diet. Investigators wanted to see if diet quality influenced eye-stalk length. They obtained the following data: d Diet Sample Mean Eye-stalk Length Variance in Eye-stalk d size, n (mm) Length (mm²) Corn (group 1) 21 2.05 0.0558 Cotton (group 2) 24 1.54 0.0812 =205-1.54-05T a) Construct a 95% confidence interval for the difference in mean eye-stalk length between the two diets (e.g., use group 1 - group 2).arrow_forwardAn article in Business Week discussed the large spread between the federal funds rate and the average credit card rate. The table below is a frequency distribution of the credit card rate charged by the top 100 issuers. Credit Card Rates Credit Card Rate Frequency 18% -23% 19 17% -17.9% 16 16% -16.9% 31 15% -15.9% 26 14% -14.9% Copy Data 8 Step 1 of 2: Calculate the average credit card rate charged by the top 100 issuers based on the frequency distribution. Round your answer to two decimal places.arrow_forward
MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSON
The Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. Freeman
Introduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman