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- Read measurements w-z on the enlarged fractional rule shown in Figure 30-13.Is the series ∑(1/(n + (1/n))), from n = 1 to infinity, comparable to the series ∑(1/(2n)), and can the comparison test be applied using 1/(2n) as the comparison function?The following ratio-to-moving averages for the seasonally adjusted series were found by the decomposition method applied on a time series representing quarterly sales for January 2018 to December 2020 period: a. Calculate the Seasonal Index for every quarter. b. If the trend is described by the trend line T^ = 1,000 + 30 t, what is the forecast for the fourth quarter of 2021?
- An operator has measured the distance between the sales centers where he will sell his product and the factory in terms of the time spent by the automobile and as a result of his evaluations, the table defining the data set in which the time between the factory and sales centers is measured in minutes is given as follows. Taking these values into account;a) Calculate the coefficient of variation of the series.b) Calculate the skewness coefficient of the series.Suppose the following are the seasonal indices for the first three quarters of the year for a quarterly series: Quarter Seasonal Index Q1 71.8 Q2 85 Q3 107.6 Remember that the seasonal indices should average 100 so you should be able to infer the seasonal index for Q4. Furthermore, suppose that the estimated coeffcients from a regression of the deseasonalized series on Time are given below: Coefficients Intercept 2,215 Time 59.3 If the original value of the series in a Q1 was 2,179, then what is the seasonally adjusted value? (please round your answer to 1 decimal place)Is the series ∑(1/(n + (1/n))), from n = 1 to infinity, comparable to the series ∑(1/(2n)) using direct comparison test?
- To see the effect of a relatively small error in the estimate of the amount of carbon-14 in a sample being dated, consider this hypothetical situation: a. A bone fragment found in central Illinois in the year 2000 contains 17% of its original carbon-14 content. Estimate the year the animal died. b. Repeat part (a), assuming 18% instead of 17%. c. Repeat part (a), assuming 16% instead of 17.Discuss the nature of the following series:Given the series:1/3 + 1/5 + 1/7 + 1/9+...is it convergent or divergent?
- The unemployment rates (%) of the four countries are as follows: 5, 8, 12, 20. What is the geometric mean of this simple series?Again, consider the geometric series 3−1+1/3−1/9+1/27−…Develop seasonal factors from the table below by following a 3-MA values for the time series data t 1 2 3 4 5 6 7 8 9 y 13 18 13 14 13 16 14 21 13
