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Confidence Intervals and Sample Size Determination: Exercises, Assignments of Mathematics

DeVry Institute of Technology & Keller Graduate School of Management - New YorkMathematics

A series of exercises focused on calculating confidence intervals and determining sample sizes for various statistical scenarios. It covers topics such as estimating population means and proportions, understanding the impact of sample size on confidence interval width, and applying statistical concepts to real-world problems. The exercises provide practical applications of confidence interval theory and sample size determination, enhancing understanding of these fundamental statistical concepts.

Typology: Assignments

2023/2024

Available from 12/18/2024

Milestonee
Milestonee 🇺🇸

4.4

(22)

3.5K documents

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WEEK 4 HOMEWORK
1.
A random sample of 100 selected from a population with a
standard deviation of 10 yielded a mean
=
225. The mean
and the standard
deviation of the distribution of the sample
means are
.
225 and 0.1
22.5 and 10
22.5 and
1
225
and 1
225 and 10
2.
Suppose a random sample of 49 is selected from a
population of size
N
=
500 with a standard deviation of 14.
If
the sample mean is 125, the 99% confidence interval to
estimate the population mean is between
.
119.85 and
130.15
120.10
and 129.90
119.85 and 135.15
118.00 and 132.00
119.85 and 129.90
3.
A manufacturer wants to purchase a certain product of foil.
The foil is stored on 1534 rolls each containing a varying
amount of foil with a standard deviation of 12.5. In order to
estimate the total number of foil on all the rolls, the
manufacturer randomly selected 200 rolls and measured the
number of foil on each roll. The sample mean was 48. Then the
95% confidence interval to estimate the population mean of foil
is between .
45.88 and 50.12
46.27 and 49.73
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Partial preview of the text

Download Confidence Intervals and Sample Size Determination: Exercises and more Assignments Mathematics in PDF only on Docsity!

WEEK 4 HOMEWORK

  1. A random sample of 100 selected from a population with a standard deviation of 10 yielded a mean = 225. The mean and the standard deviation of the distribution of the sample means are. 225 and 0. 22.5 and 10 22.5 and 1 225 and 1 225 and 10
  2. Suppose a random sample of 49 is selected from a population of size N = 500 with a standard deviation of 14. If the sample mean is 125, the 99% confidence interval to estimate the population mean is between. 119.85 and 130.15 120. and 129. 119.85 and 135. 118.00 and 132. 119.85 and 129.
  3. A manufacturer wants to purchase a certain product of foil. The foil is stored on 1534 rolls each containing a varying amount of foil with a standard deviation of 12.5. In order to estimate the total number of foil on all the rolls, the manufacturer randomly selected 200 rolls and measured the number of foil on each roll. The sample mean was 48. Then the 95% confidence interval to estimate the population mean of foil is between. 45.88 and 50. 46.27 and 49.
  1. The following random sample was selected from a normal distribution: 4.5, 6.4, 2.3, 1.8, 5.3, then the 95% confidence interval to estimate the population mean is between. 3.23 and 4.

1.62 and 6. 2.37 and 5. 4.19 and 7.

  1. A researcher is interested in estimating the mean weight of a semi trailer truck to determine the potential load capacity. She takes a random sample of 17 trucks and computes a sample mean of 20,000 pounds with sample standard deviation of 1,500. The 95% confidence interval for the population mean weight of a semi trailer truck is . 19,229 to 20, 19,365 to 20, 19,232 to 20, 18,500 to 21, 19,367 to 20,
  2. The weights of aluminum castings produced by a process are normally distributed. A random sample of 5 castings is selected; the sample mean weight is 2.21 pounds; and the sample standard deviation is 0.12 pound. The 98% confidence interval for the population mean casting weight is . 2.49 to 2. 2.08 to 2. 1.93 to 2. 2.01 to 2. 1.76 to 2.
  3. A national survey of companies included a question that asked whether the customers like the new flavor of a cola

The sample results of 1000 customers, and 850 of them indicated that they liked the new flavor. The 98% confidence interval on the population proportion of people who like the new flavor is . 0.83 and 0. 0.81 and 0. 0.84 and 0.86 0. and 0.

  1. Construct 90%, 95%, and 99% confidence intervals to estimate μ from the following data. State the point estimate. Assume the data come from a normally distributed population. 12.3 11.6 11.9 13.1 12.5 11.4 12. 11.7 11.8 12. Appendix A Statistical Tables (Round the intermediate values to 4 decimal places. Round t values to 3 decimal places. Round your answers to 2 decimal places.) 90% confidence interval: 11.79 ≤ μ ≤ 12. 95% confidence interval: 11.73 ≤ μ ≤ 12. 99% confidence interval: 11.58 ≤ μ ≤ 12. The point estimate is enter the point estimate 12.
  2. A large national company is considering negotiating cellular phone rates for its employees. The Human Resource department would like to estimate the proportion of its employee population who own an Apple iPhone. A random sample of size 250 is taken and 40% of the sample own an iPhone. The 90% confidence interval to estimate the population proportion is. 0.37 to 0.
  • 46.64 and 49.
  • 0.40 to 0.

(Round the intermediate values to 3 decimal places. Round

your answer to 3 decimal places.) 0.544 ≤ p ≤ 0. The point estimate is 0.5713.

  1. A researcher wants to determine the sample size necessary to adequately conduct a study to estimate the population mean to within 5 points. The range of population values is 80 and the researcher plans to use a 90% level of confidence. The sample size should be at least . 700 44 216 692 62
  2. An insurance company is interested in conducting a study to to estimate the population proportion of teenagers who obtain a driving permit within 1 year of their 16 th^ birthday. A level of confidence of 99 % will be used and an error of no more than .04 is desired. There is no knowledge as to what the population proportion will be. The size of sample should be at least. 160 259 289 1037 41