### Constructing a Confidence Interval for Population Standard Deviation**Problem Statement:**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.**Traffic Speeds:**```64, 63, 63, 57, 63, 53, 59, 58, 59, 70, 61, 69```**Steps to Construct the Confidence Interval:**1. **Calculate the Sample Mean & Standard Deviation:** - First, you need to find the mean (average) of the sample data. - Then, calculate the standard deviation of the sample.2. **Find the Chi-Square Critical Values:** - Access the chi-square distribution table to find the critical values for chi-square at the 95% confidence level, based on the sample size (n-1 degrees of freedom).3. **Compute the Confidence Interval Estimate for the Population Standard Deviation:** The formula to calculate the confidence interval for the standard deviation $ \sigma $ is: \[ \sqrt{\frac{(n-1)s^2}{\chi^2_{upper}}} < \sigma < \sqrt{\frac{(n-1)s^2}{\chi^2_{lower}}} \] where: - $ n $ is the sample size. - $ s $ is the standard deviation of the sample. - $ \chi^2_{upper} $ and $ \chi^2_{lower} $ are the critical values from the chi-square distribution table for the upper and lower bounds, respectively.4. **Apply the Calculations:** - Plug in the values obtained into the formula above to get the confidence interval estimate.**Interactive Table:**- Click the icon to view the table of Chi-Square critical values. This will help you find the necessary chi-square values for your calculations.**Final Output:**- The confidence interval estimate is: \[ \text{[Minimum Value]} \text{ mi/h} < \sigma < \text{[Maximum Value]} \text{mi/h} \] Ensure to round the final results to one decimal place as needed.Teaching Tip

Name: ### Constructing a Confidence Interval for Population Standard Deviat
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
Description: ### Constructing a Confidence Interval for Population Standard Deviation**Problem Statement:**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 da

Answered: Image /qna-images/answer/b18b81a8-3173-4325-8f24-8f31aa81242a.jpg

Math

Statistics

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

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

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

The following sample of 16 measurements was selected from a population that is approximately normally distributed.Construct a 90% confidence interval for the population mean.
A regional airline serving Las Vegas has a base airfare rate of $99. In addition, various fees are charged: for checked baggage, refreshments/drinks in-flight, and for making a reservation on its website. These additional charges average $70 per passenger. Suppose a random sample of 59 passengers is taken to determine the total cost of their flight. The population standard deviation of total flight cost is known to be $40. (a) What is the population mean cost per flight in dollars? $ (b) What is the probability the sample mean will be within $10 of the population mean cost per flight? (Round your answer to four decimal places.) (c) What is the probability the sample mean will be within $5 of the population mean cost per flight? (Round your answer to four decimal places.)
In a random sample of 5 mobile devices, the mean repair cost was $60.00 and the standard deviation was $12.00. Assume the population is normally distributed and use a t-distribution to find the margin of error and construct a 95% confidence interval for the population mean. Interpret the results.
The mean tar content of a simple random sample of 25 unfiltered king-size cigarettes is 21.4 mg, with a standard deviation of 3 mg. The mean tar content of a simple random sample of 25 filtered 100-mm cigarettes is 13.0 mg with a standard deviation of 3.8 mg. The accompanying table shows the data. 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. Let population 1 be unfiltered king-size cigarettes. Complete parts (a) through (c) below. Click the icon to view the data. a. Use a 0.05 significance level to test the claim that unfiltered king-size cigarettes have a mean tar content greater than that of filtered 100-mm cigarettes. What does the result suggest about the effectiveness of cigarette filters? Identify the null and alternative hypotheses. O B. Ho: H1 =H2 O C. Ho: H1 #H2 H1: H1 =H2 O A. Ho: H1 = H2 H:H1 H2 O F. Ho: H1 = H2 H1:H1> H2 H:H1=H2 Hq: H1…
A random sample of 8 adults aged 30 years were asked how much they spent on medical costs in the year 2009. Using the following data, compute the sample mean, the sample standard deviation, the sample median, and the first and third quartiles. 300 140 5600 520 470 700 640 1200
A single burger contains a mean of 100 g of cooked beef with a standard deviation of 5 g. The restaurant owner claims that new triple burger contains three times as much beef. The table shows a sample of masses from 30 triple burgers. Does the sample support the claim at a 95% confidence level? Triple Burger Beef Mass (g) 292 297 295 290 290 294 291 296 282 291 289 291 290 292 295 289 289 294 298 292 294 295 285 297 296 287 302 289 290 290
A report stated that after obtaining a bachelor's degree, 43% of college students enroll in a graduate degree program. For a random sample of 61 undergraduate students, find the mean, variance and standard deviation for the number of students who will enroll in a graduate degree program after obtaining a bachelor's degree. a.) mean b.) variance c.) standard deviation (round to two decimal places)
A manufacturer advertises that the average life of batteries produced by his firm is at least 12 months. The consumer board disagrees, and claims that the average life of the batteries is less than 12 months. The consumer board test a random sample of 9 batteries and find that the mean life is 10.6 months with a standard deviation of 2. The consumer board's alternative hypothesis is: A. The average life of the population of batteries is 12 months. B. The average life of the population of batteries is less than 12 months. C. The average life of the population of batteries is more than 12 months. D. The average life of the population of batteries is at least 12 monthsThe manufacturer of 'Road King' tyres claim that their tyres last an average of 70,000km or more. The Consumer Board suspects that this claim may be false (they have received some complaints) and decide to test the manufacturer's claim. The Consumer Board took a sample of size 500 from the population. They ran the…
A study was conducted for an aviation safety agency in which they surveyed thousands of passengers at airports across Europe. In this study, the "mass" for a passenger includes the weight of the passenger and all of the passenger's carry-on items, including infants without their own seats. For the 5,904 adult male passengers measured in summer, the sample mean and standard deviation for this mass were 88.8 kg and 15.9 kg, respectively. (a) Construct a 95% confidence interval (in kilograms) for the population mean mass for adult male passengers in summer. (Round your answers to three decimal places.) ___to__ kg (b) Write a sentence or two interpreting the confidence interval you found in part (a). With 95% confidence, we can estimate that the population mean mass of male passengers traveling in the summer is contained within the interval. We can estimate that 95% of the male passengers traveling in the summer in the sample have a mass that is contained within the interval.…
A survey finds that the prices paid for two-year-old Ford Fusion cars are normally distributed with a mean of $17,500.00 and a standard deviation of $500.00. Consider a sample of 10,000 people who bought two-year-old Ford Fusions. 6800 of the people who bought two-year old Ford Fusions spends between $ .00 and $ .00 How many people spends less than $17,000.00 people. How many people spends more than $19,000.00 people (Note this question has to do with the empirical rule and the symmetric nature of the normal distribution)
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
The salaries of professional baseball players are heavily skewed right with a mean of $3.2 million and a standard deviation of $2 million. The salaries of professional football players are also heavily skewed right with a mean of $1.9 million and a standard deviation of $1.5 million. A random sample of 40 baseball players’ salaries and 35 football players’ salaries is selected. The mean salary is determined for both samples. Let represent the difference in the mean salaries for baseball and football players. Which of the following represents the shape of the sampling distribution for ? skewed right since the populations are both right skewed skewed right since the differences in salaries cannot be negative approximately Normal since both sample sizes are greater than 30 approximately Normal since the sum of the sample sizes is greater than 30