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1 of 3 ID: MST. FET.E.CIMSU.01.0010A [4 marks Internet company Gurgle is carrying out testing on the efficiency of its search engine. A sample of 40 searches have been carried out and the time taken to display the results has been recorded for each search. The mean search time for the sample was calculated as 0.2474 seconds. The standard deviation of the search times for the sample was calculated as 0.0163 seconds. The population standard deviation of search times is unknown. Gurgle a) Select all the techniques that are commonly used to construct a confidence interval for the mean when the population standard deviation () is unknown: Approximate the population standard deviation () with the sample standard deviation (s) Replace the sample size (n) with n-1 Decrease the confidence level to compensate for the increased margin of error Approximate the standard normal distribution with the Student's t distribution b) Calculate the upper and lower bounds of the 95% confidence interval for the mean search time for the Gurgle search engine. You may find this Student's t distribution table useful. Give your answers in seconds to 4 decimal places. Upper bound = seconds Lower bound = seconds 2 of 3 ID: MST.FET.E.CIMSU.02.0020A [1 mark] A team of software engineers are testing the 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 31 times are collected. The mean time in this sample is 880.7 seconds and the sample standard deviation is found to be 51.2. Calculate the 95% confidence interval for the mean time taken to execute the algorithm. You may find this Student's t distribution table useful. Give your answers to 2 decimal places. SUS 3 of 3 ID: MST.FET.E.CIMSU.03.0010A [1 mark] Tyler and Jack are both studying a numerical variable X. Both 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% confidence interval. Each student will collect their own sample, but both samples will have 30 items in them. When constructing his confidence 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 the sample standard deviation, s, and uses this in his confidence interval. However as it turns 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: O it is impossible to tell which confidence interval will be wider Jack's confidence interval will be wider than Tyler's both confidence intervals will be of the same width Tyler's confidence interval will be wider than Jack's
