The national Menso organisation would like to estimate the average I.Q. of its members. A sample of 60 members complete an I.Q. testr and achieve an average score of 144. The standard deviation in this sample is 5.85. The population standard deviation is unknown. menso a) Select all the techniques that are commonly used to construct a condence interval for the mean when the population standard INIERNAHONAL deviation (o) is unknown: D Approximate the population standard deviation (0) with the sample standard deviation [5) D Replace the sample size {n} with n-1 D Decrease the condence level to compensate for the increased margin of error D Approximate the standard normal distribution with the Student's t distribution b) Calculate the upper and lower bounds of the 95% condence interval for the average LQ. in Mensa. You may nd this Student's t distribution table useful. Give your answers to 2 decimal places. Upper bound = \\:| :| Lower bound = A team of software engineers are testing tire time taken for a particular type of modern computer to execute a complicated algorithm for factoring large numbers. They would like to estimate the mean time taken for a computer to execute the algorithm. A random sample of 41 times are collected. The mean time in this sample is 645.6 seconds and the sample standard deviation is found to be 81.0. Calculate the 90% condence interval for the mean time taken to execute the algorithm. You may nd this Student's t distribution table useful. Give your answers to 2 decimal places. Tyler and Jack are botir studying a numerical variable X. Bolir students want to estimate the population mean of this variable, 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, o. 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. As it turns out, the sample standard deviation that Jack calculates tums out to be slightly less than the value assumed by Tyler for the population standard deviation. Based on this information, it is true to say that: Tyler's condence interval will be wider than Jack's both condenoe intervals will be of the same width it is impossible to tell which condence interval will be wider Jack's condenoe interval will be wider than Tyler's OOOO
