Additional Practice 1. For each of the following situations, define the parameter (using a symbol and words) and set up appropriate null and alternative hypotheses about it. The parameter has been defined for you in the first problem: a. Under normal conditions, 64% of the seeds of the rare plant Botanica statistica germinate. Scientists at an agricultural research station believe that application of a certain vitamin formulation may increase the germination rate. p = the proportion of all seeds of Botanica statistica that will germinate if the vitamin formulation is applied Ho: Ha: b. A government agency reports that the proportion of automobiles that come off of assembly lines without significant manufacturing flaws is 96%. A consumer organization suspects that the actual figure is lower than this. p = Ho: Ha: c. Nationally, 8% of homeowners get their house painted in any given year. A random sample of California homeowners is taken to see if the percentage is different from the national figure. p = Ho: Ha: 2. Suppose we select a random sample of 100 Math 140 students and find that 43% said they believe in love at first sight. Mark each statement as True or False: a. There were 43 students in the sample who said they believe in love at first sight. b. Based on the information in the sample, we cannot determine exactly what proportion of the population of all Math 140 students would say they believe in love at first sight. C. p = 0.43 d. p = 0.43 953. In a recent Gallup Poll, about 50% of the respondents said they believed in love at first sight. Let p be the proportion of all college students who believe in love at first sight. a. What null and alternative hypotheses do you think would be appropriate? b. Using either the information from Problem #2 or the responses to Question #23 of the class questionnaire from your own class, perform a test of significance using a significance level of a = 10%. c. State your conclusion in context. d. Are you completely comfortable with your conclusion? (Hint: Was the sample drawn from the indicated population?) 964. Currently, about 10% of marriages in the United States end in divorce during the first five years of marriage. A sociologist is studying the effect on the divorce rate of having children within the first two years of marriage. Using hospital birth records, she selected a random sample of 100 couples who had a child within the first two years. Following up on these couples, she finds that 17 of these couples had divorced within the first five years. a. Set up appropriate null and alternative hypotheses to test whether having children within the first two years of marriage affects the divorce rate. Assume having children could either increase or decrease the divorce rate. b. Calculate the value of the test statistic. c. Determine the p-value of the test. d. Suppose a test is performed using a significance level of a = .05. Based on your answer to (c), would we reject the null hypothesis? What could we conclude, if anything, about the effect on the divorce rate of having children within the first two years of marriage? 975. Understanding the p-value: A university administrator guesses that about 20% of the students at her 98 school had sent a text message during class at least once. The head of the Faculty Senate believed that the percentage is higher than that, so he conducted a survey of randomly selected students. 28% of the students surveyed admitted to having sent a text message during class at least once. Using the survey data, a test of significance of Ho: [7 =20 versus Ha: p >.20 gave a p-Value of 3%. a. Give a correct interpretation of this pvalue by lling in the blanks in the statement below: \"If the true proportion of students who have texted during class is 20%, then the that a survey like this would result in 28% or 7' of the students admitting to having texted during class is b. Does this give strong evidence or weak evidence that the head of the Faculty Senate was right in thinking that more than 20% of students at her school have texted during class at least once? Carefully explain the reasoning behind your