ZuoTi.Pro
Question

21. Given a sample of family incomes (in $) as below: 53,600 97,700 65,000 110,400 47,300...

21. Given a sample of family incomes (in $) as below: 53,600 97,700 65,000 110,400 47,300 77,000 84,700, 38,800 76,200 120,000 63,400 89,600 (21.a) Calculate the sample mean. (Show the Excel formula you use.) (21.b) Calculate the sample standard deviation. (Show the Excel formula you use.) (21.c) Calculate E at 95% confidence level for the population mean. (Show the Excel formula you use.) (21.d) Calculate the 95% confidence interval for the population mean. (21.e) If you want a narrower confidence interval, you need to ________ sample size. a. increase b. decrease

math   Statistics-And-Probability   
0 0
Add a comment Improve this question Transcribed image text
Next > < Previous
Sort answers by oldest

Homework Answers

Answer #1

(a) The fomula for calculating the sample mean is 12 53600+97700+...+89600) (923700) (923700) 76975 76975 Therefore, the sample mean is X 76975 The formul a for calculating the sample mean is using the Excel2010 function is → AVERAGE (A23: A34) Therefore, the sample mean is X~ 76975 (b) The fomula for calculating the sample stan dard deviation is using the Excel2010 function is STDEV (Entire range of the data) Therefore, the standard deviation iss24917.29 c) The formula for calculating the margin of error is using the Excel2010 functi on is CONFIDENCE.T (Entire range of the data) Therefore, the margin of error is E 1583169

(d) The sample m ean is X- 76975 The sample size is n 12. The sample standard deviation is s-24917.29 The degrees of freedom is df n-1 =12-1 The level of significance is α-0.05 The table values are cal culated by using the excel function tinv(probability, deg rees of freedom) =tinv(0.05, 11) 2.20098516 2.20098516 The formula for calculating the 95% confidence interval for the population mean is 24917.29 24917.29 76975+1002511 24917 2976975+oosau 3464102 3.464102 24917.29 76975-(2.20098516) 76975-(2.200985 16) (71 93.000859) AS 76975 +4025u (7193.000859) 76975-1583 1.688 15 μ 76975+1583 1.688 15 61 143.31 185,s μ 92806.688 15 x-4-1 susẵthi 4-1 -61 143. 31 191 μ 928066882 : 61143 31 19|SAS|92806 6882| Interpretatıon We can be 95% confident that the population mean is between 61143.3119 and 92806.6882 (e) Explanati on If it is to get the narrower confi dence interval, then it is better to increase the sample size. As the sample size increases, the width of the confidence interval becomes naffower Hence, the correct alternative 1s (a

0 0
Add a comment
Know the answer?
Add Answer to:
21. Given a sample of family incomes (in $) as below: 53,600 97,700 65,000 110,400 47,300...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions

  • A sample of 100 family incomes has a mean of $100,000 with a standard deviation of...

    A sample of 100 family incomes has a mean of $100,000 with a standard deviation of $10,000. The 95% confidence interval estimate for the mean of the population is : Group of answer choices $90,000 to $110,000 $98,350 to $101,650 $81,400 to $119,600 $98,040 to $101,960.

  • You are given the sample mean and the population standard deviation. Use this information to construct...

    You are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confidence ntervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If convenient, use technology to construct the confidence intervals A random sample of 45 home theater systems has a mean price of $138.00. Assume the population standard deviation is 516.40. Construct a 90% confidence interval for the population mean. The 90% confidence interval...

  • AM You are given the sample mean and the population standard deviation. Use this information to...

    AM You are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If convenient, use technology to construct the confidence intervals. A random sample of 35 home theater systems has a mean price of $144.00. Assume the population standard deviation is $15.60. Construct a 90% confidence interval for the population mean. The 90% confidence...

  • 4. The monthly incomes from a random sample of workers in a factory are shown below....

    4. The monthly incomes from a random sample of workers in a factory are shown below. Monthly Income (In $1,000) 4.0 5.0 7.0 4.0 6.0 6.0 7.0 9.0 a. Compute the standard error of the mean (in dollars). b. Compute the margin of error in dollars) at 95% confidence. c. Complute a 95% confidence interval for the mean of the population. Assume the population has a normal distribution. Give your answer in dollars.

  • The monthly incomes from a random sample of workers in a factory are shown below. Monthly...

    The monthly incomes from a random sample of workers in a factory are shown below. Monthly Income, in $1,000 4.0 5.0 7.0 5.0 6.0 6.0 10.0 8.0 9.0 (Please, avoid rounding intermediate steps and round your final solutions to at least 2 decimal places) Compute the 95% confidence interval for the mean monthly incomes of the workers. Provide the lower and upper bound of the interval below and give your answer in dollars. Are there any additional assumptions needed in...

  • In a certain town, a random sample of executives have the following personal incomes (in thousands);...

    In a certain town, a random sample of executives have the following personal incomes (in thousands); 35 43 29 55 63 72 28 33 36 41 42 57 38 30 Assume the population of incomes is normally distributed. Find the 95% confidence interval for the mean income.

  • to estimate the population mean repair cost of microwave ovens in macomb, a random sample of...

    to estimate the population mean repair cost of microwave ovens in macomb, a random sample of 9 broken microwave ovens was selected and it is found that the sample mean repair cost was $80 with a sample standard deviation of $15. 1) what would be the “critical value” if you want to find a 95% confidence interval for the population mean? 2) what would be the “margin of error” if you want to find a 95% confidence interval for the...

  • 21. Calculate the 95% Confidence interval around a sample mean of 100, based on a sample...

    21. Calculate the 95% Confidence interval around a sample mean of 100, based on a sample NE 25 with a (population standard deviation) o = 10. (4 points)

  • A random sample of 24 observations is used to estimate the population mean. The sample mean...

    A random sample of 24 observations is used to estimate the population mean. The sample mean and the sample standard deviation are calculated as 128.4 and 26.80, respectively. Assume that the population is normally distributed. [You may find it useful to reference the t table.) a. Construct the 95% confidence interval for the population mean. (Round intermediate calculations to at least 4 decimal places. Round "t" value to 3 decimal places and final answers to 2 decimal places.) Confidence interval...

  • 2. After conducting a census in 1970, the family incomes in a certain city were found...

    2. After conducting a census in 1970, the family incomes in a certain city were found to have a mean of $14,200 with a standard deviation of $2600. A random sample of 75 families taken in 1975 produced x¯ = $14, 930 (in 1970 dollars, after adjusting for inflation). Assume throughout this problem that the standard deviation of family incomes is the same in 1975 as it was in 1970. a) Identify each of the numbers $14200, $2600, and $14930...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT