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The scores of 50 students are given below. 95 82 88 101 82 110 129 115 81 104 78 85 74 107 113 84 93 115 66 97 85 95 66 80 123 82 110 179 81 70 116 67 121 120 119 97 112 113 82 108 73 92 102 100 88 110 65 78 110 (a) Construct a frequency distribution for the data. Use 65-74 for the first class and use 10 for the cla A study was done to look at the relationship between number of vacation days employees take each year width for each subsequent class. and the number of sick days they take each year. The results of the survey are shown below. Class Frequency Vacation Days 14 3 6 8 8 65-74 Sick Days 0 7 2 0 4 1 0 2 8 6 a. Find the correlation coefficient: r = Round to 3 decimal places . b. The null and alternative hypotheses for correlation are: Ho: ? = 0 H1 : 2 0 The p-value is: Round to 4 decimal places. C. Use a level of significance of a = 0.05 to state the conclusion of the hypothesis test in the context of the study. There is statistically significant evidence to conclude that an employee who takes more vacation days will take fewer sick days than an employee who takes fewer vacation days There is statistically significant evidence to conclude that an employee who takes more vacation days will take more sick days than an employee who takes fewer vacation days. There is statistically insignificant evidence to conclude that there is a correlation between the number of vacation days taken and the number of sick days taken. Thus, the use of the A CBS News poll conducted June 10 and 11, 2006, among a nationwide random sample of 651 adults, asked regression line is not appropriate. those adults about their party affiliation (Democrat, Republican or none) and their opinion of how the US There is statistically significant evidence to conclude that there is a correlation between the economy was changing ("getting better," "getting worse" or "about the same"). The results are shown in the number of vacation days taken and the number of sick days taken. Thus, the regression line is table below. useful. d. The equation of the linear regression line is: y = better same worse T (Please show your answers to 3 decimal places) Republican 38 104 Democrat 12 87 137 e. Predict the number of sick days taken for an employee who took 3 vacation days this year. Remember none 21 118 to only use the model if you found that there is linear relationship between the variables. Otherwise, you should use the average of the y-values. Sick Days = (Please round your answer to the nearest whole number.) Express your answers as a decimal and round to the nearest 0.001 (in other words, type 0. 123, not 12.3% or 0. 123456). If we randomly select one of the adults who participated in this study, compute: P(Republican) = P(worse) = P(worse | Republican) = P(Republican | worse) = P(Republican and worse) = An experiment is run. The mass of an object is recorded over time. A well-known brokerage firm executive claimed that 90% of investors are currently confident of meeting their investment goals. An XYZ.Investor Optimism Survey, conducted over a two week period, found that in Time (min) Mass (g) 16 42 a sample of 500 people, 87% of them said they are confident of meeting their goals. 24 39 27 22 Test the claim that the proportion of people who are confident is smaller than 90% at the 0.025 significance 48 21 12 The null and alternative hypothesis would be: Plot the points in the grid below. Ho:u 0.9 45 H1:4 > 0.9 H1:p > 0.9 H1:u # 0.9 H1:p