The different interest rates charged by some financial institutions may reflect how stringent their standards are for their loan appraisals: the lower the rate, the higher the standards, and hence, the lower the default rate. The data below were collected from a sample of eight financial companies selected at random. Financial company Interest rate (in %) x Default rate (in 1000 loans) y 12 3 45 7.0 50 7 6.6 6.0 8.5 8.0 7.5 6.5 7.0 56 58 48 45 49 46 47 al Find the least square regression line. b/ Perform the test Ho: Bi = 0, HA: BI + 0 (using a = 0.05) to determine whether there is enough evidence to infer that a linear dependence exists between interest rate (x) and default rate (y).
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- Consider the historical return data of ABC portfolio as below. 1990 4% 1991 10% 1992 2% 1993 1% 1994 5% 1995 -1% 1996 7% 1997 -3% 1998 0% 1999 3% What is the sample (empirical) probability that return is greater than or equal to 4%? Why? What is the average return given that the return is greater than or equal to 4%?The accompanying table shows, for a random sample of 20 long-term-growth mutual funds, percentage return over a period of 12 months and total assets (in millions of dollars).Return Assets Return Assets Return Assets29.3 300 16.0 421 12.9 7527.6 70 15.5 99 11.3 61023.7 3,004 15.2 756 9.9 26422.3 161 15.0 730 7.9 2722.0 827 14.4 436 6.7 7119.6 295 14.0 143 3.3 71917.6 29 13.7 117a. Calculate the Spearman rank correlation coefficient.b. Carry out a nonparametric test of the null hypothesis of no association in the population against a two-sided alternative.c. Discuss the advantages of a nonparametric test for these data.Borrowing money may be necessary for business expansion. However, too much borrowed money can also mean trouble. Are developing countries tending to borrow more? A random sample of 20 developing countries gave the following information regarding foreign debt per capita (in U.S. dollars, inflation adjusted). (Reference: Handbook of International Economic Statistics, U.S. Government Documents.) Country 1 2 3 4 5 6 7 8 9 10 Modern Debt per Capita 173 156 122 128 99 81 35 22 22 84 Historic Debt per Capita 141 138 89 116 58 67 34 32 44 74 Country 11 12 13 14 15 16 17 18 19 20 Modern Debt per Capita 26 24 16 25 197 183 141 127 109 77 Historic Debt per Capita 25 11 17 21 107 154 149 119 116 76 Does this information indicate that foreign debt per capita is increasing in developing countries? Use a 0.01 level of significance. (a) What is the level of significance? (b) Compute the sample test statistic. (Round your answer to two decimal places.) (c) Find the P-value of the…
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- The following payoff table was developed. Let the probability of state of natures are as follows:P(S1) = 0.30, P(S2) = 0.40, and P(S3) = 0.30. Compute the expected monetary value for each of the alternatives. What decision would you recommend? Alternative S1 S2 S3A1 80 92 94A2 82 80 85A3 67 70 72A4 45 69 54According to the IRS, individuals filing federal income tax returns prior to March 31 received an average refund of $1056 in 2018. Consider the population of “last-minute” filers who mail their tax return during the last five days of the income tax period (typically April 10 to April 15). A researcher suggests that a reason individuals wait until the last five days is that on average these individuals receive lower refunds than do early filers. For a sample of 400 individuals who filed a tax return between April 10 and 15, the sample mean refund was $910. Based on prior experience, a population standard deviation of σ = $1,600 may be assumed. Test the researcher's assertion using the critical value approach. Use α = 0.05 (Please include all the 7 steps in hypothesis testing) Steps in hypothesis testing p-value Approach Develop the null and alternative hypothesis Specify the level of significance, α Choose the test statistic (z or t) Calculate the test statistic Use the value of the…An auditor detects that a firm is regularly overstating the amounts of inventories because of delays in recording withdrawals. He takes a random sample of 20 inventories and finds that they are overstated by the following amounts (in pounds sterling) 10 12 9 28 6 20 26 24 12 22 5 14 11 23 9 21 29 13 16 24 An auditor detects that a firm is regularly overstating the amounts of inventories because of delays in recording withdrawals. He takes a random sample of 20 inventories and finds that they are overstated by the following amounts (in pounds sterling). 10 12 9 28 6 20 26 24 12 22 5 14 11 23 9 21 29 13 16 24 (a) Make a relative frequency table of the data using groups 5−9, 10−14, . . . technically, such groups are known as bins. (b) Draw a frequency histogram of the data. (c) Describe the shape of the distribution of the data, commenting on any interesting features. (d) Calculate the sample mean and the sample median, and compare these two values. Which of these two…