Download Introduction to Chance Models (Section 1.1) Introduction A key step

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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 Güntürkün’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 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 (𝜋) 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 don’t 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