**Commuting to work:** A community survey sampled 1923 people in Colorado and asked them how long it took them to commute to work each day. The sample mean one-way commute time was 25.5 minutes with a standard deviation of 13 minutes. A transportation engineer claims that the mean commute time differs from 25 minutes. Do the data provide convincing evidence that the engineer's claim is true? Use the $ \alpha = 0.05 $ level of significance and the critical value method with the [Critical Values for the Student's t Distribution Table](#).---**Part: 0 / 5**---**Part 1 of 5**(a) State the appropriate null and alternate hypotheses.\[ H_0: \]\[ H_1: \]This hypothesis test is a (Choose one) ▼ test.**Graph Explanation:**There is a selection box for choosing the hypothesis symbols. The symbols include:- Less than ($<$)- Less than or equal to ($\leq$)- Greater than ($>$)- Greater than or equal to ($\geq$)- Not equal to ($\neq$)- Equal to ($=$)- Mu ($\mu$)There are also buttons for selection ($ \times $) and reset ($ \circlearrowleft $).

Answer - A transformation engineer claims that the mean commute time differs from 25 minutes.…

Answered: Commuting to work: A community survey…

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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You may need to use the appropriate technology to answer this question. The Insure.com website reports that the mean annual premium for automobile insurance in the United States was $1,503 in March 2014. Being from Pennsylvania at that time, you believed automobile insurance was cheaper there and decided to develop statistical support for your opinion. A sample of 25 automobile insurance policies from the state Pennsylvania showed a mean annual premium of $1,425 with a standard deviation of s = $160. (a) Develop a hypothesis test that can be used to determine whether the mean annual premium in Pennsylvania is lower than the national mean annual premium. Ho: HS 1,503 H: µ > 1,503 Ho:H > 1,503 H: µ< 1,503 H0: μ2 1,503 H3: H< 1,503 Ho:H< 1,503 H.: μ2 1,503 Ho: H = 1,503 H: µ # 1,503 (b) What is a point estimate in dollars of the difference between the mean annual premium in Pennsylvania and the national mean? (Use the mean annual premium in Pennsylvania minus the national mean.) (c) At a…
The use of chemicals is considered to increase the resistance to scratches during a painting process. The average durability was found to be 7.5 br and the standard deviation was found to be 1.5 br for the 15 parts painted using item A. The average durability was found to be 8.8 br and the standard deviation was found to be 1.2 br for the 12 parts painted using item B. What is the value of the test statistic calculated in the test that will be performed to determine which substance to choose? Determine it at the 99% confidence level with the assumption that the anacuttle variances are equal.Answer options group A)- 1,21 B) -4.68 C)- 3.26 D)-2.44
Suppose that water usages in American showers are normally distributed, with an average shower using 16.4 gallons, and a standard deviation of 3.7 gallons. Estimate the percentage of showers that used between 9 and 23.8 gallons more than 27.5 gallons less than 12.7 gallons between 9 and 20.1 gallons
An economist would like to estimate the mean amount of money that a family spends towithin $30. If the amount spent by a family is considered to be normally distributed withstandard deviation $250, what sample size would be necessary to be 93% confident?
A hospital president claims that the average Salary of registered nurses at her hospital is more than $57,000. You test this claim by surveying 37 registered nurses at this hospital and find they have a mean salary of $57,425. Assume the population standard deviation is $1750 at the 0.10 level of significance is there enough evidence to support the claim of the hospital president?
Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous for cutthroat trout. Suppose a friend tells you that the average length of trout caught in Pyramid Lake is μ=20 inches. However, a survey reported that of a simple random sample of 37 fish caught, the mean length was 17.5 inches, with an estimated standard deviation of 4.3 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than μ=20 inches? Use α=0.05. What is the value of the test statistic? (Round your answer to two decimal places.)Find the P-value. (Round your answer to four decimal places.)Based on your results, will you reject or fail to reject the null hypothesis? Are the data statistically significant at level αα? A) At the α=0.05α=0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. B) At the α=0.05α=0.05 level, we reject the null hypothesis and conclude the data are statistically significant. C)…
what measure of variability is to be computed with a median
An instructor claims that the average number of hours needed to study for a final exam in order to pass should be 5 hours. A student believes that the instructor is understating the number of hours needed to pass and surveys 36 students and finds the sample mean and standard deviation to be 5.7 and 1.5 hours respectively. Test the instructors claim at a .10 level.
A student in public administration wants to determine the mean amount members of city councils in large cities earn per month as remuneration for being a council member. The error in estimating the mean is to be less than $120 with a 95 percent level of confidence. The student found a report by the Department of Labor that estimated the standard deviation to be $900. What is the required sample size?
An industrial engineer is conducting a time study for a work element. The select time is 4.5 minutes, and the sample standard deviation of the observed time is 20 seconds. What is the appropriate sample size if the estimate is to be 5 percent of the true average time 95 percent of the time?
An economist would like to estimate the mean amount of money that a family spends towithin $35. If the amount spent by a family is considered to be normally distributed withstandard deviation $261, what sample size would be necessary to be 91% confident?
Humerus bones from the same species of animal have approximately the same length-to-width ratios. It is known that Species A has a mean ratio of 5.9. Suppose that 100 fossil humerus bones were unearthed at a site where Species A is known to have flourished. (We assume that all bones are from the same species.) The length-to-width ratios of these bones have a sample mean 5.6 and sample standard deviation 0.25. Can we conclude that the mean ratio of these bones is significantly smaller than those of Species A? Test with a 0.01 significance level. What is the standard error?

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