"he Police Department is investigating the need for a speed camera to be implemented on Swift Road. A sample of 55 cars passing through tiiat road on a particular day were randomly selected and their speeds recorded. The speed limit on Swift Road" Is 6-0 miles per hour (mph). The mean speed for tiie sample was calculated as 4? mph. 'he standard deviation of the speeds for tire sample was calculated as 4 mph. The standard deviation for the population of cars driving on Swift Road" Is unknown. a) Select all the techniques that are commonly used to construct a condence interval for the mean when the population standard deviation (0) is unknown: D Approximate the population standard deviation {o} with the sample standard deviation [5) D Replace the sample size {n} with n1 D Approximate the standard normal distribution with the Student's t distribution D Decrease the condence level to compensate For the increased margin of error b) Calculate the upper and lower bounds of the 99% condence interval for the mean speed traveled on Swift Road. You may nd this Student's t distribution table useful. Give your answers in mph to 2 decimal places. Upper bound = E mph E Lower bound = mph A psychologist has developed an aptitude test which consists of a series of mathematical and vocabulary problems. They are interested in determining the mean score for the test. A random sample of 31 people have taken the test and the mean test score for the sample is 245. The sample standard deviation for this group is 6.1. Calculate the 90% condence interval for die mean test score. You may nd this Student's t distribution table useful. ve your answers to 2 decimal places. Tyier and Jack are both studying a numerical variable X. BotiI students want to estimate the population mean of this valiable, and they each intend to collect a sample, calculate a sample mean and construct a 95% condence interval. Each student will collect their own sample, but both samples will have 30 items in them. when constructing his condence interval, Tyler assumes a value for the population standard deviation, 1:. In contrast, Jack does not assume a value for the population standard deviation. Jack calculates tire sample standard deviation. s, and uses this in his condence interval. However as it tums out, the sample standard deviation that Jack calculates turns out to be equal to the value assumed by Tyler for the population standard deviation. Based on this information, it is true to say that: it is impossible to tell which condence interval will be wider Jack's condence interval will be wider than Tyler's Tyler's condenoe interval will be wider than Jack's 0000 both condenoe intervals will be of the same width
