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Statistics

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_______________________________________________________________________ A study of 8 worldwide financial institutions showed the correlation between their assets and pretax profit to be .74. (1) State the decision rule for .01 significance level: Ho: ρ ≤ 0; H1: ρ > 0 (rounded 3 decimal places.) Reject Ho if t> (2) Compute the value of the test statistic. (Rounded to 2 decimal places.) Value of the test statistic (3) Can we conclude that the correlation in the population is greater than zero? Use the .01 significance level Reject or Do not reject Ho . It is reasonable or not reasonable to conclude that there is positive association in the population between assets and pretax profit. __________________________________________________________________ The following sample observations were randomly selected. (Do not round the intermediate values. Rounded to 2 decimal places.) X: 4 5 3 6 10 Y: 9.7 5 8.9 14.3 23.5 (a) Determine the 0.95 confidence interval for the mean predicted when X = 9 ( , ) (b) Determine the 0.95 prediction interval for an individual predicted when X = 9 ( , ) ____________________________________________________________________ Given the following hypothesis: H0 : μ = 130 H1 : μ ≠ 130 A random sample of six resulted in the following values 141, 142, 137, 145, 148, and 144. Using the .05 significance level, can we conclude the mean is different from 130? (a) What is the decision rule? (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) Reject H0 : μ = 130 and fail to reject H1 : μ ≠ 130 when the test statistic is (Click to select)outside the intervalinside the interval ( , ). (b) The value of the test statistic is (Round your answer to 3 decimal places.) ) What is your decision regarding H0 ? Reject or Fail to reject (d) Estimate the p-value. Greater than 0.1Between 0.05 and 0.2Less than 0.001Between 0.001 and 0.05 _________________________________________________________________________ In a poll to estimate presidential popularity, each person in a random sample of 1,390 voters was asked to agree with one of the following statements: 1. The president is doing a good job. 2. The president is doing a poor job. 3. I have no opinion. A total of 750 respondents selected the first statement, indicating they thought the president was doing a good job. (a) Construct a 95 percent confidence interval for the proportion of respondents who feel the president is doing a good job. (Round your answers to 3 decimal places.) Confidence interval for the proportion is up to . (b) Based on your interval in part (a), is it reasonable to conclude that a majority (half) of the population believes the president is doing a good job? YesNo ____________________________________________________________________ Waterbury Insurance Company wants to study the relationship between the amount of fire damage and the distance between the burning house and the nearest fire station. This information will be used in setting rates for insurance coverage. For a sample of 30 claims for the last year, the director of the actuarial department determined the distance from the fire station (X) and the amount of fire damage, in thousands of dollars (Y). The MegaStat output is reported below. ANOVA table Source SS df MS F Regression 1,875.5782 1 1,875.5782 42.33 Residual 1,240.4934 28 44.3033 Total 3,116.0716 29 Regression output Variables Coefficients Std. Error t(df=28) Intercept 12.5908 3.1151 3.547 Distance-X 2.6222 7.347 6.51 -------------------------------------------------------------------------------- (a-1) Write out the regression equation. (Round your answers to 3 decimal places.) Y = + X. (a-2) Is there a direct or indirect relationship between the distance from the fire station and the amount of fire damage? The relationship between distance and damage is (Click to select)inversedirect. (b) How much damage would you estimate (in dollars) for a fire 6 miles from the nearest fire station? (Round your answer to the nearest dollar amount. Omit the "$" sign in your response.) Estimated damage $ (c-1) Determine the coefficient of determination. (Round your answer to 3 decimal places.) Coefficient of determination (c-2) Fill in the blank below. % of the variation in damage is explained by variation in distance.