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3) You want to see if the proportion of female college students who are majoring in the sciences is statistically different then the proportion of male college students who are majoring in the sciences. You take a sample of 50 female college students and find that 18 of them are majoring in the sciences. You take a sample of 60 male college students, and find that 55% of them are majoring in the sciences. At the 5% significance level, is there sufficient evidence that there is a difference in the proportion of female and male college students who are majoring in the sciences: (10 points) Population 1: Population 2: Data: Write the null and alternate hypothesis in symbols: Null: Alternate: Critical Value(S): Test Statistic: p-value: initial conclusion: reason: Formal conclusion:1) The data below shows the scores a sample of husbands and their wives received when given a happiness test to determine their 'happiness' in the relationship. (10 points) Couple 1 2 3 4 5 6 7 8 9 10 Husband|50 65 72 18 45 98 77 85 50 82 Wives 60 55 60 25 80 80 70 80 70 50 Run a Hypothesis test to determine if there IS linear correlation in the population of all husbands and wives at the 5% significance level: You may use any appropriate hypothesis test method. State Hypothesis (in symbols): Null: Alternate: Test Statistic: Critical value(s): Initial conclusion: Formal Conclusion: Find the regression line (even if there isn't correlation in the population) Write the meaning of the slope of the regression line: Find the best predicted score a wife would have, if her husband scored 50