### Statistical Analysis: Confidence Intervals**Scenario:**49 packages are randomly selected from packages received by a parcel service. The sample has a mean weight of 24.0 pounds. Assume that the standard deviation \( \sigma = 2.0 \) pounds. What is the 95% confidence interval for the true mean weight, \( \mu \), of all packages received by the parcel service?**Options:**- 23.3 to 24.7 pounds- 23.4 to 24.6 pounds- 23.5 to 24.5 pounds- 23.2 to 24.8 pounds**Explanation:**A confidence interval is a range of values that is likely to contain the population mean with a certain level of confidence. This problem requires calculating a 95% confidence interval for the mean weight of all packages, using the sample mean and standard deviation provided.**Calculations:**To calculate the confidence interval, we use the formula for the confidence interval of the mean:\[\bar{x} \pm Z \left( \frac{\sigma}{\sqrt{n}} \right)\]Where:- \( \bar{x} \) is the sample mean- \( Z \) is the Z-score corresponding to the desired confidence level (1.96 for 95%)- \( \sigma \) is the population standard deviation- \( n \) is the sample size**Visual Explanation:**The image has no graphs or diagrams to explain, so focus is purely on textual explanation of the statistical concept of confidence intervals.

The sample mean The population standard deviation The sample size For 95% confidence interval Z…

Answered: 49 packages are randomly selected from…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Listed below are speeds (mi/h) measured from traffic on a busy highway. This simple random sample was obtained at 3:30 P.M. on a weekday. Use the sample data to construct a 95% confidence interval estimate of the population standard deviation. 64 63 63 57 63 53 59 58 59 70 61 69
An experiment was conducted to determine whether giving candy to dining parties resulted in greater tips. The mean tip percentages and standard deviations are given in the accompanying table along with the sample sizes. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b). OA. Ho: H₁ H₂ H₁: H₁ H₂ OC. Ho: H₁ H₁: H₁ C a. Use a 0.05 significance level to test the claim that giving candy does result in greater tips. What are the null and alternative hypotheses? H₂ H₂ No candy Two candies B. Ho: M₁ = H₂ H₁: H₁ H₂ D. Ho: H₁ μ H₁ H₂ H₂ H₁: M₁
Listed in the accompanying table are heights (in.) of mothers and their first daughters. The data pairs are from a journal kept by Francis Galton. Use the listed paired sample data, and assume that the samples are simple random samples and that the differences have a distribution that is approximately normal. Use a 0.05 significance level to test the claim that there is no difference in heights between mothers and their first daughters. Mother 64.0 66.0 63.0 62.0 66.5 66.0 65.0 60.0 67.0 63.0 Daughter 67.0 66.5 70.5 66.0 61.0 66.0 65.5 65.0 67.0 65.0 In this example, Hd is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the daughter's height minus the mother's height. What are the null and alternative hypotheses for the hypothesis test? Ho: Ha = 0 in. H₁ Hd 0 in. (Type integers or decimals. Do not round.) Identify the test statistic. t= (Round to two decimal places as needed.)
Tina catches a 14-pound bass. She does not know the population mean or standard deviation. So she takes a sample of five friends and they say the last bass they caught was 9, 12, 13, 10, and 10 pounds. Find the t and calculate a 95% (α = .05) confidence interval.
Discuss the difference between the 95% and 99% confidence levels. What are the corresponding alpha levels and how confident is the researcher in the results? Edit View Insert Format Table 12pt ✓ | P ▸ Paragraph B IU A ✓T²✓ 岬くく描く To B √x www 11 ✓
Determine whether the following statement is true or false. To construct a confidence interval about the mean, the population from whlch the sample is drawn must be approximately normal. This statement is
Find 90% confidence interval
Researchers studied the mean egg length (in millimeters) for a bird population. After taking a random sample of eggs, they obtained a 95% confidence interval of (45,60). What is the value of the margin of error? Choose the correct answer below. A. 15 mm B. 52.5 mm O c. 7.5 mm O D. 1.96
Listed below are systolic blood pressure measurements (mm Hg) taken from the right and left arms of the same woman. Assume that the paired sample data is a simple random sample and that the differences have a distribution that is approximately normal. Use a 0.05 significance level to test for a difference between the measurements from the two arms. What can be concluded? Right arm Left arm 151 136 120 134 134 181 174 180 156 138 In this example, Ha is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the measurement from the right arm minus the measurement from the left arm. What are the null and alternative hypotheses for the hypothesis test? O A. Ho: Hd = 0 O B. Ho: Hd 0 O C. Ho: Hd = 0 O D. Ho: Hd 0 H1: Ha>0
K In a random sample of eleven people, the mean driving distance to work was 22.3 miles and the standard deviation was 4.9 miles. Assume the population is normally distributed and use the t-distribution to find the margin of error and construct a 95% confidence interval for the population mean u. Interpret the results. Identify the margin of error. (Round to one decimal place as needed.) Construct a 95% confidence interval for the population mean. (Round to one decimal place as needed.) Interpret the results. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) OA. It can be said that % of the population has a driving distance to work (in miles) that is between the interval's endpoints. O B. % of all random samples of eleven people from the population will have a mean driving distance to work (in miles) that is between the interval's endpoints. OC. With % confidence, it can be said that most driving distances…

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