[5133 35:? In May 2017, researchers found from a random sample of n=755 US cell phone users age 18 and older that the average number of text messages sent or received per day is 41.5 messages. with a margin of error of 5.2 messages. What is the correct calculation for the interval estimate for the mean number of text messages? 0 41.5 2 x 5.2 to 41.5 + 2 x 5.2 0 41.5 2 to 41.5 + 2 G) 41.5 755 to 0.46 + I755 O 41.5 5.2 to 41.5 + 5.2 [5134 353 Suppose we collect data from a random sample of 1,000 Penn State students and use it to build a condence interval for the correlation between number of hours typically spent watching television per day and GPA. The 95% condence interval is from -0.21 to -0.05. Select the statement below that correctly interprets this condence interval. 0 95% of the population correlations between number of hours typically spent watching television per day and GPA will fall between 0.21 and 0.05. O The probability that the population correlation between number of hours typically spent watching television per day and GPA is between 0.21 and 0.05 is 0.95. 0 We are $596 condent that the sample correlation between number of hours typically spent watching television per day and GPA is between 0.21 and 0.05. 0 We are 95% condent that the population correlation between number of hours typically spent watching television per day and GPA is between 0.21 and 0.05. 10 7 5 3 53 Suppose a researcher surveys 100 college students asking them the maximum amount of money they would be willing to spend on a date. The mean amount reported is $73.50, and 5,000 bootstrap samples were used to construct a 95% confidence interval for the population mean, which is calculated to be 66.50 to 80.50. Indicate what would happen to the width of the confidence interval if the changes below were made. For each option, assume all other quantities are held constant. The sample size is changed from 100 students to 500 students Width would increase The number of bootstrap samples used is changed from 5,000 to [ it14 ] V 10,000 The confidence level is changed from 95% to 99% V The sample mean is changed from 73.50 to 54.00 [ #614 ] V10 5 6 3 5 You are in a lab with 150 students. Each student takes a sample from the same bead box containing red and black beads. Each student uses the same method to compute a confidence interval for the population proportion of red beads in the box based on their sample. The confidence intervals of about 20% of students fail to contain the true proportion of red beads. Of the options below, what is the best choice for the confidence level of the confidence intervals created by the students in this lab? O 20% O 80% O 10% O 95%