The sample mean response time in the northern part of the town is
The sample standard deviation of the response time in the northern part of the town is
The degree of freedom is = 30 - 1 = 29
The critical value of t is = 2.045
The 95% confidence interval for the mean response time in the northern part of the town is
The 95% confidence interval for the mean response time in the northern part of the town is
On plotting the points, we get the following curve
The curve is very slightly skewed, and hence we can use the confidence interval. The sample size of at least 30 is required. Here, that criteria is satisfied, and the curve looks approximately like a normal curve, hence it would be okay to proceed like that it calculating the confidence inetrval.
The correct option is (3).
First option is incorrect because the curve is almost symmetric and the sample size is also sufficiently large.
Second option is incorrect because the curve is not extremely skewed.
Fourth option is incorrect because the t-distribution is not always safe to use. It is not safe to use if the distribution is extremely skewed.
Thank You!! Please Upvote!!
One of the two fire stations in a certain town responds to calls in the northern...
One of the two fire stations in a certain town responds to calls in the northern half of the town, and the other fire station responds to calls in the southern half of the town. The following is a list of response times (in minutes) for both of the fire stations (this data will be used for several problems). Both samples may be regarded as simple random samples from approximately normal populations so that the t- procedures are safe to...
#1. One of the two fire stations in a certain town responds to calls in the northern half of the town, and the other fire station responds to calls in the southern half of the town. The following is a random sample of response times (in minutes) for the fire station that responds to calls in the northern half of the town. Please note that the data have been written in order to simplify by-hand calculations. Northern: 3,3,3,3, 4, 4,...
One of the town council members believes that the two fire stations have different mean response times. Do you agree? Why? Use a significance level of 0.05 and the p-value to make your decision. Again, the data for both stations has been re-copied for convenience. Northern: 3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,6,7,7, 8, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10,12 Southern: 4,4,4,4,5,5,5,5,5,5,5,6,6,7.7.8, 8, 8, 8, 8, 8, 9, 10, 10, 10, 12, 12. 12, 12, 13 Answer in the blanks to show...
One of the town council members believes that the two fire stations have different mean response times. Do you agree? Why? Use a significance level of 0.05 and the p-value to make your decision. Again, the data for both stations has been re-copied for convenience. Northern: 3,3,3,3,4,4,4,4,4,5,5,5,5,5,5, 6, 7, 7, 8, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10, 12 Southern: 4,4,4,4,5,5,5,5,5,5,5, 6, 6, 7, 7, 8, 8, 8, 8, 8, 8, 9, 10, 10, 10, 12, 12,...
Question 2 (4 points) A stem plot for the response times of the fire station that responds to calls in the northern part of town has been constructed below. Key: 1/2 = 12 minutes 0/3 3 3 3 014 4 4 4 4 5 5 5 5 5 5 016 7 7 08 8 8 8 8 9 9 110 000 112 Comment on the shape of the distribution and determine appropriate measures of center and spread. 1. extremely skewed...
1. (20 points total) A small town receives radio broadcast from two radio stations, a news station (N) and a music station (M). Of the listeners who are tuned to the news station, 75% will remain listening to news after the station break that occurs each half hour, while the other listeners wll switch to the music station at the station break. Of the listeners who are tuned to the music station, 40% will switch to the news station at...
A fire insurance company wants to see if the amount of fire damage (y) in major residential fires is related to the distance between the residence and the nearest fire station (x). The study is to be conducted in a large suburb of a major city, a sample of 15 recent fires in this suburb is selected. The 15 values and the printout follow: A) State the Null and Alternative Hypotheses. In Excel B) Construct a scatter diagram for the...
The accompanying data contain the rating of large and medium size airports in a particular country, based on a 1000-point maximum. Complete parts (a) through (d) below . a. For large and medium airports separately, construct a 95% confidence interval estimate for the population mean rating The 95% confidence interval estimate for the population mean rating for large size airports is nothing less than or equals≤muμless than or equals≤nothing. (Round to the nearest integer as needed.) The 95% confidence interval...
The following ANOVA model is for a multiple regression model with two independent variables: Degrees of Sum of Mean Source Freedom Squares Squares F Regression 2 60 Error 18 120 Total 20 180 Determine the Regression Mean Square (MSR): Determine the Mean Square Error (MSE): Compute the overall Fstat test statistic. Is the Fstat significant at the 0.05 level? A linear regression was run on auto sales relative to consumer income. The Regression Sum of Squares (SSR) was 360 and...
Page 1 Question 1 Suppose we take repeated random samples of size 20 from a population with a Select all that apply. mean of 60 and a standard deviation of 8. Which of the following statements is 10 points true about the sampling distribution of the sample mean (x)? Check all that apply. A. The distribution is normal regardless of the shape of the population distribution, because the sample size is large enough. B. The distribution will be normal as...