3/9/2016 Stats 250 W16 HW 5 Closing date: 3/10/16 5:00PM Question 1 : 56e01f0490e76e0b00b39e12 0.5 point(s) CLT: True or False? The Central Limit Theorem (CLT) guarantees that the sample mean is normally distributed whenever the population size is sufficiently large, even if the underlying population distribution is skewed. Question 1 Multiple Choice Options True False Question 2 Background : Watching Television The amount of time Americans spend watching television is closely monitored by firms such as A.C. Nielsen because this helps to determine advertising pricing for commercials. According to American Time Use Survey, the distribution of the variable \"time spent watching television on a weekday\" for American adults is skewed to the right with population mean of 2.35 hours per day and standard deviation of 1.93 hours per day Question 2 Subquestions 2.a 0 point(s) Suppose an American adult is selected at random. What can be said about the probability that the person watches TV for at least 4.13 hours a day on a weekday? about 0.9906 about 0.9732 about 0.8212 about 0.1788 It cannot be determined accurately from the information given. 1/10 3/9/2016 2.b 1 point(s) Suppose a random sample of 36 adult Americans will be selected, the time spent watching television on a weekday will be recorded for each, and the sample mean time spent watching television on a weekday will be computed. What can be said about the probability that the sample mean time spent watching television on a weekday will be more than 3.18 hours? about 0.9993 about 0.9951 about 0.0049 It cannot be determined accurately from the information given. Question 3 Background : Too Fast a Location? At a particular location along a highway, a state official from the Department of Transportation in an unmarked car records the speed for each of a random sample of 36 cars. The resulting sample mean speed was 68.3 miles per hour (mph), and the standard error of the sample mean was 1.18 mph. Question 3 Subquestions 3.a 0 point(s) It is assumed that the sample of cars is randomly selected (representative). Even though the histogram and QQ plot of the 36 car speeds are found to show evidence that the population of speeds at that location may not be normally distributed, can the resulting confidence interval be considered valid? Yes No Question 4 Background : Social Networks The use of social networks, for example, Facebook and Twitter, has grown dramatically all over the world. In a recent survey among social network users, it was reported that Indonesians and Saudi Arabians spend the most time per day using social networks. American social network users reportedly spend over 3 hours per day social 2/10 3/9/2016 networking from a computer, tablet, and/or mobile phone. A random sample of 24 American social network users was obtained and each was asked for the amount of time spent (in hours) social networking each day. The sample mean is 3.19 hours with a standard deviation of 0.2903 hours. Question 4 Subquestions 4.a 0 point(s) The sample mean of 3.19 hours is an estimate of the population mean time that Americans spend social networking (in hours) per day. Report the standard error of the sample mean (include your units). Student answer No answer entered. 4.b 1 point(s) Provide a 90% confidence interval estimate for , the population mean number of hours that Americans spend social networking per day. Report to two decimal places and include units. Note: you can assume that the distribution of the number of hours that Americans spend social networking per day is approximately normal. Student answer No answer entered. 4.c 0 point(s) Provide an appropriate interpretation of the 90% confidence interval in context. Student answer No answer entered. 4.d 1 point(s) Which of the following interpretations regarding the 90% confidence level are correct? Select all that are correct. If the procedure is repeated many times, we would expect about 90% of the resulting confidence intervals to contain the sample mean number of hours that Americans spend social networking per day. If the procedure is repeated many times, we would expect about 90% of the resulting confidence intervals to contain the population mean number of hours that Americans spend social networking per day. If the procedure is repeated many times, 90% of the time the interval computed in the previous part will contain the population mean number of hours that Americans spend social networking per day. 3/10 3/9/2016 If the procedure is repeated many times, then we'd expect the population mean number of hours that Americans spend social networking per day to fall in 90% of the resulting 90% confidence intervals. Question 5 Background : Fire Drill An engineering company claims that the mean time it takes an employee to evacuate a building during a fire drill is less than 60 seconds. You want to test this claim. A random sample of 50 employees was collected, and their evacuation times (in seconds) are provided in the file FireDrill.RData (https://pbjcoursework.s3.amazonaws.com/Intro%20to%20Statistics/instructor/11-19-2015/3_23_727-1_51_54FireDrill.RData) (and also FireDrill.csv (https://pbjcoursework.s3.amazonaws.com/Intro%20to%20Statistics/instructor/11-19-2015/3_25_662-20_54_349FireDrill.csv)). Question 5 Subquestions 5.a 0 point(s) Before conducting the hypothesis test of interest, you need to determine if all conditions are met. Clearly state the additional condition that is required to be able to perform the one-sample t-test. (Note: include context when you state the additional condition.) Student answer No answer entered. 5.b 1 point(s) Create both a histogram and a QQ plot to check the remaining condition. Include the graphs as images and briefly explain whether the condition appears to be reasonably met. Student answer No answer entered. 5.c 0 point(s) Test the following hypotheses about the population mean fire drill evacuation time in seconds: H0 : = 60 seconds versus Ha: < 60 seconds. Copy and paste the One-Sample T Test results below or save the test output as a jpg and add it in as an image to your answer text box. Below the output, clearly report the t-test statistic value and the p-value for this test in the answer text box. 4/10 3/9/2016 Student answer No answer entered. 5.d 1 point(s) What distribution was used to find the p-value for the t-test? standard normal N(0, 1) distribution normal distribution with mean of 49 and a standard deviation of 21.5122 a t(50) distribution a t(49) distribution 5.e 1 point(s) Based on the resulting p-value, what decision and conclusion should you make at a 5% significance level? Fail to reject the null hypothesis and conclude that the population mean fire drill evacuation time in seconds is not significantly lower than 60 seconds. Fail to reject the null hypothesis and conclude that the population mean fire drill evacuation time in seconds is significantly lower than 60 seconds. Reject the null hypothesis and conclude that the population mean fire drill evacuation time in seconds is not significantly lower than 60 seconds. Reject the null hypothesis and conclude that the population mean fire drill evacuation time in seconds is significantly lower than 60 seconds. Question 6 Background : California Crime Rate Back in 2005, California reported an average of 6511 crimes (per 100,000 residents) for its various counties. A research group in California decided to assess if the average crime rate for the year 2010 (the most recent year data is available) appears to have increased over the 6511 (per 100,000) by taking a random sample of 84 counties and measuring for each the number of crimes (per 100,000) for the year 2010. The data have been provided in the Rdata set called crime.Rdata (https://pbj- 5/10 3/9/2016 coursework.s3.amazonaws.com/Intro%20to%20Statistics/instructor/11-19-2015/3_36_421-15_3_245crime.Rdata). You have been asked to use the data to test (at a 10% level) the following hypotheses: H0: = 6511 versus Ha: > 6511. Question 6 Subquestions 6.a 0 point(s) The hypotheses involve the parameter . Is this definition for the parameter correct or incorrect? \" = the population average crime rate (number of crimes per 100,000 residents) reported in 2010 for all counties in California.\" Correct Incorrect 6.b 1 point(s) Generate the R Commander output to perform the t test (use a test value of 6511). Copy the one-sample test output from R Commander and paste it in as your answer. Student answer No answer entered. 6.c 0 point(s) Which of the following are the correct values for the test statistic and p-value to test the desired hypotheses? t = 2.1394 and p-value = 0.07 t = 2.1394 and p-value = 0.035 t = 2.1394 and p-value = 0.01767 t = -2.1394 and p-value = 0.98233 6.d 1 point(s) At the 10% significance level which of the following is the correct statistical decision and conclusion? Reject H0 and conclude there is sufficient evidence to say the population average crime rate appears to have increased over the 6511 (per 100,000). 6/10 3/9/2016 Fail to reject H0 and conclude there is sufficient evidence to say the population average crime rate for 2010 appears to have increased over the 6511 (per 100,000). Reject H0 and conclude there is not sufficient evidence to say the population average crime rate for 2010 appears to have increased over the 6511 (per 100,000). Fail to reject H0 and conclude there is not sufficient evidence to say the population average crime rate for 2010 appears to have increased over the 6511 (per 100,000). Question 7 : 0.5 point(s) Time Plots Check IID True or False: Suppose that a set of data has been collected over time. A time plot of the data set shows an increasing trend. This means that we have evidence that the observations are not iid (independent, identically distributed). Question 7 Multiple Choice Options True False Question 8 Background : Watches Consider the following hypotheses: H0: The watch is waterproof. Ha: The watch is not waterproof. Think about what would be a Type 1 and a Type 2 error for these hypotheses. Question 8 Subquestions 8.a 0 point(s) In this situation, which error would be worse? Type 1 error 7/10 3/9/2016 Type 2 error 8.b 1 point(s) Provide a brief sentence to explain the consequence(s) of such an error. Make sure that your explanation is in context. Student answer No answer entered. Question 9 : 1 point(s) Freshman Placement Test The following statement is FALSE. "If a model for scores on a placement test for incoming freshmen is skewed left and a large number of such students (say n = 200) is randomly selected, then the model for placement test scores will become approximately normal." According to the Central Limit Theorem, which of the following would have approxiately a normal distribution in this situation? Question 9 Multiple Choice Options the individual placement test scores for freshmen the population mean placement test score for all freshmen the sample mean placement test score for all freshmen Question 10 Background : Response Time During a medical emergency, people who dial 911 expect an ambulance to arrive quickly and personnel to provide vital care. A random sample of ambulance response times in minutes were collected. A 95% confidence interval for the population mean response time for ambulances is found to be 7.5 minutes to 9.5 minutes. Question 10 Subquestions 10.a 8/10 3/9/2016 0 point(s) What is the sample mean for the response time? 7.5 minutes 8.5 minutes 9.5 minutes Cannot be determined 10.b 1 point(s) A fixed level of significance of 5% was selected to test the hypotheses minutes. What would be your statistical decision? minutes vs. Reject H0 Fail to Reject H0 Cannot Tell 10.c 0 point(s) A fixed level of significance of 10% was selected to test the hypotheses minutes. What would be your statistical decision? minutes vs. Reject H0 Fail to Reject H0 Cannot Tell 10.d 1 point(s) A fixed level of significance of 10% was selected to test the hypotheses minutes. What would be your statistical decision? minutes vs. Reject H0 Fail to Reject H0 Cannot Tell 9/10 3/9/2016 Edit Assignment (/#!/students/56bdda16f22d490b003bafbe/do) 56e01f0490e76e0b00b39e12 10/10