### Manual Transmission AutomobilesIn a recent year, 6% of cars sold had a manual transmission. A random sample of college students who owned cars revealed the following: out of 130 cars, 21 had manual transmissions. Estimate the proportion of college students who drive cars with manual transmissions with 99% confidence. Round intermediate and final answers to at least three decimal places.#### Calculation DetailsTo find the confidence interval, we will use the following formula for the proportion's confidence interval:\[ \hat{p} \pm Z_{\alpha/2} \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} \]- \(\hat{p}\) = Sample proportion = \(\frac{x}{n}\) - \(x\): number of manual transmission cars (21) - \(n\): total number of cars (130)- \(Z_{\alpha/2}\): Z-value for 99% confidence level (Approximately 2.576)#### Steps1. **Calculate sample proportion (\(\hat{p}\))**: \[ \hat{p} = \frac{21}{130} \]2. **Calculate the standard error (SE)**: \[ SE = \sqrt{\frac{\hat{p}(1 - \hat{p})}{130}} \]3. **Multiply the Z-value by the standard error** to find the margin of error (ME): \[ ME = Z_{\alpha/2} \times SE \]4. **Construct the confidence interval**: \[ (\hat{p} - ME, \hat{p} + ME) \]By completing these steps, we can accurately determine the requested confidence interval for the proportion of college students who drive cars with manual transmissions.#### Graphical ExplanationThere are no graphs or diagrams provided in the given image. If there were any, they would typically illustrate the normal distribution with the confidence interval marked on the bell curve, showing the central proportion and the tails representing the significant regions defined by the Z-value.This guide presents a detailed explanation of how to estimate the proportion and construct a confidence interval that can be used in instructional material on an educational website.

Name: ### Manual Transmission AutomobilesIn a recent year, 6% of cars sold
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: ### Manual Transmission AutomobilesIn a recent year, 6% of cars sold had a manual transmission. A random sample of college students who owned cars revealed the following: out of 130 cars, 21 had manual transmissions. Estimate the proportion of colle

Obtain the 99% confidence interval for the true proportion of college students who drive cars with…

Math

Statistics

Manual Transmission Automobiles In a recent year, 6% of cars sold had a manual transmission. A random sample of college students who owned cars revealed the following: out of 130 cars, 21 had manual transmissions. Estimate the proportion of college students who drive cars with manual transmissions with 99% confidence. Round intermediate and final answers to at least three decimal places.

Manual Transmission Automobiles In a recent year, 6% of cars sold had a manual transmission. A random sample of college students who owned cars revealed the following: out of 130 cars, 21 had manual transmissions. Estimate the proportion of college students who drive cars with manual transmissions with 99% confidence. Round intermediate and final answers to at least three decimal places.

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

A random sample of 1067 teenagers (ages 12 to 17) were asked whether they played games online; 787 said that they did. What is the size of the sample? I What is the value (±0.001) of the statistic p? .
The CEO of a large electric utility claims that at least 80 percent of his one million customers are very satisfied with the service they receive. A local newspaper surveyed 300 customers randomly. 73 percent said they were very satisfied. The test statistic is (Round answer to two decimal places. Do not write 0.12 as .12.)
In a recent year, 6% of cars sold had a manual transmission. A random sample of college students who owned cars revealed the following: out of 124 cars, 25 had manual transmissions. Estimate the proportion of college students who drive cars with manual transmissions with 90% confidence. Round intermediate and final answers to at least three decimal places.
(12) adults said they would travel to outer space in their lifetime, given the chance. Estimate the true proportion of adults who would like to travel to outer space with 88% confidence (Round to two decimal places). Estimate population proportion: New York Times poll found that 329 out of 763 12
Claim: Most adults would erase all of their personal information online if they could. A software firm survey of 508 randomly selected adults showed that 55% of them would erase all of their personal information online if they could. Find the value of the test statistic. The value of the test statistic is (Round to two decimal places as needed.) --
Can you find and show the p-value for this question?
A B This graph has an r of -0.5. C D
According to an expert for the automotive industry, 68% of Americans know how to drive a manual transmission vehicle. Suppose 220 Americans are sampled. (Give results accurate to at least 4 decimal places.) a. Of the 220 people sampled, 160 respond that they know how to drive a manual transmission vehicle. What is the sample statistic p? p = b. Under the assumption that the industry expert's claim that 68% of Americans know how to drive a manual transmission vehicle is valid, what is the probability that the survey in part (a) would result in a p that is at least as high as the one found? c. Under the assumption that the industry expert's claim that 68% of Americans know how to drive a manual transmission vehicle is valid, what is the probability that the survey in part (a) would result in a p that is between 66% and 71%?
PrActicE the legalization of marijuana. Among the Democratic voters surveyed, 158 of the 200 people aged 18-29 and 210 of the 300 people aged 50-64 supported legalizing marijuana. Is this difference significant at a = .05? A random sample of individuals in one town was surveyed about their position on
According to a sociologist's research on U.S. residents' habits regarding religious faith, 38% of U.S. residents attend a religious service (any denomination) at least once per month. Suppose 310 U.S. residents are sampled. (Give results accurate to at least 4 decimal places.) a. Of the 310 people sampled, 132 respond that they attend a religious service at least once per month. What is the sample statistic p? p= 0.4258 b. Under the assumption that the sociologist's claim that 38% of U.S. residents attend a religious service at least once per month is valid, what is the probability that the survey in part (a) would result in a p that is at least as high as the one found? c. Under the assumption that the sociologist's claim that 38% of U.S. residents attend a religious service at least once per month is valid, what is the probability that the survey in part (a) would result in a p that is between 37% and 40%?
Among freshmen at a certain university, scores on the Math SAT followed the normal curve, with an average of 550 and an SD of 100. Fill in the blank. A student who scored 430 on the Math SAT was at the ____th percentile of the score distribution. Answer the problem by entering a value between 0 and 100 without % to fill in the blank. Any correctly rounded answer will receive full credit.
A random sample of 1000 college applications showed that 625 of those applications were submitted online. Compute the test statistic used to test the claim that among all college applications the percentage submitted online is equal to 65%. Round your answer to three decimal places.