The Central Limit Theorem (CLT) guarantees that the sample mean is normally distributed whenever thepopulation 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. Nielsenbecause 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 tothe right with population mean of 2.35 hours per day and standard deviation of 1.93 hours per day Question 2 Subquestions 2.a Suppose an American adult is selected at random. What can be said about the probability that the personwatches TV for at least 4.13 hours a day on a weekday? about 0.9906 about 0.9732 about0.8212 about 0.1788 It cannot be determined accurately from the information given. 2.b Suppose a random sample of 36 adult Americans will be selected, the time spent watching television on aweekday 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 aweekday 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 unmarkedcar records the speed for each of a random sample of 36 cars. The resulting sample mean speed was 68.3miles per hour (mph), and the standard error of the sample mean was 1.18 mph. Question 3 Subquestions 3.a 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 arecent survey among social network users, it was reported that Indonesians and Saudi Arabians spend themost time per day using social networks. American social network users reportedly spend over 3 hours per daysocial networking from a computer, tablet, and/or mobile phone. A random sample of 24 American socialnetwork users was obtained and each was asked for the amount of time spent (in hours) social networkingeach day. The sample mean is 3.19 hours with a standard deviation of 0.2903 hours. Question 4 Subquestions 4.a 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 answerNo answer entered.4.b1 point(s)Provide a 90% confidence interval estimate for µ, the population mean number of hours that Americans spendsocial networking per day. Report to two decimal places and include units. Note: you can assume that thedistribution of the number of hours that Americans spend social networking per day is approximately normal. 4.c Provide an appropriate interpretation of the 90% confidence interval in context. 4.d 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. 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 6 Subquestions 6.a The hypotheses involve the parameter μ. Is this definition for the parameter correct or incorrect?“μ = the population average crime rate (number of crimes per 100,000 residents) reported in 2010 for allcounties in California.” Correct Incorrect 6.b Generate the R Commander output to perform the t test (use a test value of 6511). Copy the onesample testoutput from R Commander and paste it in as your answer= 6.c Which of the following are the correct values for the test statistic and pvalue to test the desired hypotheses? t = 2.139 and pvalue = 0.07 t = 2.139 and pvalue = 0.035 t = 2.139 and pvalue = 0.0175 t = 2.139 and pvalue = 0.9825 6.d 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 tohave increased over the 6511 (per 100,000). Fail to reject H0 and conclude there is sufficient evidence to say the population average crime rate for2010 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 2010appears 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 for2010 appears to have increased over the 6511 (per 100,000). Question 7 : 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 anincreasing trend. This means that we have evidence that the observations are neither independent noridentically distributed. True False Question 8 Background : Watches Consider the following hypotheses:H : The watch is waterproof.H : 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 In this situation, which error would be worse? Type 1 error Type 2 error 8.b Provide a brief sentence to explain the consequence(s) of such an error. Make sure that your explanation is incontext. 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 What is the sample mean for the response time? 7.5 minutes 8.5 minutes 9.5 minutes Cannot be determined 10.b A fixed level of significance of 5% was selected to test the hypotheses minutes vs.minutes. What would be your statistical decision? Reject H0 Fail to Reject H0 Cannot Tell 10.c A fixed level of significance of 10% was selected to test the hypotheses minutes vs.minutes. What would be your statistical decision? Reject H0 Fail to Reject H0 Cannot Tell 10.d A fixed level of significance of 10% was selected to test the hypotheses minutes vs.minutes. What would be your statistical decision? Reject H0 Fail to Reject H0 Cannot Tell