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5. Conduct a simulation analysis (using the One Proportion applet) to assess the strength of evidence that the sample data provide for GÃ¼ntÃ¼rkÃ¼nâs conjecture that kissing couples tend to lean their heads to the right more often than they would by random chance. Report the approximate p-value and summarize your conclusion about this strength of evidence. Your simulation analysis should convince you that the sample data provide very strong evidence to believe that kissing couples lean their heads to the right more than half the time in the long run. That leads to a natural follow-up question: How much more than half the time? In other words, we have strong evidence that the long-run probability of leaning to the right is greater than one-half, but can we now estimate the value for that probability? We will do this by testing many different (null) values for the probability that a couple leans to the right when kissing. 6. Now test whether the data provide evidence that the long-run probability that a couple leans their heads to the right while kissing (ð) is different from 0.60. Use the One Proportion applet to determine the p-value for testing the null value of 0.60. Report what you changed in the applet and report your p-value. Think about it: What kind of test are we conducting if we want to determine whether the population parameter is different from a hypothesized value - a one-sided test or a two-sided test? Remember from Section 1.4 that if we donât have a specific direction we are testing, greater than or less than, we need to use a two-sided test of significance. If you used a one-sided alternative in #8, determine the two-sided p-value now by checking the Two-sided box. Recall that a p-value of 0.05 or less indicates that the sample data provide strong evidence against the null hypothesis and in favor of the alternative hypothesis. Thus, we can reject the null hypothesis when the p-value is less than or equal to 0.05. Otherwise, when the p-value is greater than 0.05, we do not have strong enough evidence against the null hypothesis and so we consider the null value to be plausible for the parameter. Key Idea: We will consider a value of the parameter to be plausible if the two-sided p-value for testing that parameter value is larger than the level of significance. 7. Is the p-value for testing the null value of 0.60 less than 0.05? Can the value 0.60 be rejected, or is the value 0.60 plausible for the long-run probability that a couple leans their heads to the right while kissing? June 27, 2014 MAA PREP workshop 57