Please solve this. First questions are based on histogram.
Histogram 20 Haawncy 3 This assignment refers to the Histogram shown on the above that depicts the distribution of a set of quiz scores. Q 1 requires application of learning from Module 9 combined with new learning from Module 10. ts 2-6 require your interpretation of the Histogram. NOTE: You must answer ALL of the following questions to receive full points. and to have your attendance recorded for Week 10. 1. Suppose it is known that the standard deviation of the length of time to complete a particular manufacturing task is 90 seconds. If the manufacturer wants to estimate the total completion time at a condence level of 99% with a margin of error of 1 second, how many measurements should be included in the sample? Justify your answer with a calculation. 2. A random sample of B-week-old kittens from a certain population is weighed. Here are the kittens' weights, in grams: 1465 1335 1305 1330 1390 1440 1255 1360 1300 1235 1335 1265 1370 1345 1415 1405 1295 1365 1380 1240 1265 1320 1395 1205 1335 1330 1265 a} State the sample mean and sample standard deviation. 6} Plot the sample data in a histogram. Do the sample data appear roughly Normally distributed? Comment on its suitability for use in a condence interval. You may refer to the sample size to support your argument. c} Calculate a 95% condence interval. Show the formula and values used. Interpret the condence interval in the context of the data (state the interval in a sentence}. d] In light of your answer to [b], do you believe that this condence interval is a reliable way of estimating the mean weight of 3-week-old kittens from the population? Explain briefly. 3. It is accepted that the scores on the Calibrated-Sprint Fitness Test were Normally distributed with an average completion time of 52 seconds and a standard deviation of 8 seconds. A sports therapist decides to test whether barefoot runners have the same average completion time as the general population. She designs a randomized experiment and obtains the following summary statistics: 11 = 32. J? = 56 seconds. Is there evidence at the tr. = 0.31 level to suggest that barefoot runners have a different average completion time from the general population? Your answer should contain: - a clear statement of null and alternative hypotheses - calculation of a test statistic (including the formula used} a statement and interpretation of the p va|ue in terms of statistical significance (you do not need to justify how you found the p value} - a conclusion that interprets the p va|ue in the context of this research problem. 4. A researcher wishes to test the theory that the proportion of people who spend money on microtransactions in a certain mobile game has increased from its historical 22%. Suppose that a sample of 233 players contains 61 who have recently made a microtransaction. Does this data support the theory that more than 22% of players make microtransactions? Assume the distribution is normal, and test at the a = 0.05 level. Your answer should contain: - a clear statement of null and alternative hypotheses - calculation of a test statistic (including the formula used] a statement and interpretation of the p va|ue in terms of statistical significance (you do not need to justify how you found the p value) - a conclusion that interprets the p va|ue in the context of this research
