CW 19.1. Age at first marriage. The histogram below shows the distribution of ages at First marriage of 5.534 randomly sampled women between 2U06 and 2010 in the USA. The average age at first marriage of these women is 23.44 with a standard deviation of 4.72. 1000 Bill] 600 400 200 D llIIllIl 'ID 15 2E] 25 3C! 35 41] 45 Age at rst man'iage (a) Estimate the average age at first marriage of women using a 95% confidence interval. Give your answer to three decimal places. [2] [b] Provide an explanation (in one sentence} of what this confidence interval tells us from this example. [1] (c) Discuss if conditions required for the method you used to calculate your confi- dence interval have been satisfied (max one sentence for each). [3] CW 19.2. Online communication. A study suggests that the average university student spends 2.25 hours per week communicating with others online. You believe that this is an un- derestimate and decide to collect your own sample for a hypothesis test. You randomly sample 90 students from your accommodation and find that on average they spent 2.75 hours a week communicating with others online. A friend of yours, who offers to help you with the hypothesis test. comes up with the following set of hypotheses. Indicate any errors you see. [3] H0 : f c: 2.25 hours HA : i > 2.75 hours