7. Conduct a simalation analysis (using the One Proportion applet) to assess the

Question

7. Conduct a simalation analysis (using the One Proportion applet) to assess the strength of evidence that the sample data provide for Gintürkin's 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 summarise your conclusion about this strength of evidence. Your simulation analysis should convince you that the sample data provide very strong ev dence to believe that kissing couples lean their heads to the right more than half the time in the long ran. 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 proportion of kissing couples who lean to the right is greater than 1/2, but can we now estimate the value for that probability? We will do this by testing many different (muall) values for the probability that a couple leans to the right when kissing. 8. Now test whether the data provide evidence that the probability that a couple leans their heads to the right while kissing (a) 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-aone-sided test or a two-sided test? Remember from Section 1.4 that if we dont 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 basx Recall from Section 2.3 that we can specify a level of significance in order to decide whether the p-value is small. For example, we can say a p-value of 0.05 or less is strong evi- dence 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 9. Is the p-value for testing the null value of 0.60 less than 0.05? Can the value 0.60 be rejee- ted, or is the value 0.60 plausible for the probablity that a couple leans their heads to the right while kissing? MacBook Air

Explanation / Answer

Answer to the question#1)

The observation units of this study are the couples who kiss each other

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Answer to the question#2)

The variable being recorded is the side the head turns while kissing. The head may turn either on the right side or the left side, this makes this variable categorical

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Answer to question#3)

In this scenario the value being calculated is based on the sample and hence it is a statistic. If the value relates to the entire population only then it is called parameter

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Answer to question#4)

The observed number of couples = 124

But the information about how many of these couples turn their head to right is not provided in the question and hence the exact value of pie cannot be calculated given the data in the content above.

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