Certainly! Here is a detailed transcription and explanation suitable for an educational website:---### Statistical Analysis: Ear Wiggling Among Millionaires**Context:** Only about 13% of the general population can wiggle their ears. A survey conducted with 364 millionaires revealed that 40 of them could wiggle their ears. We aim to determine if the proportion of ear-wiggling among millionaires is significantly different from the general population, using a significance level of \(\alpha = 0.01\).#### Steps for Hypothesis Testing:**a. Test Selection** - For this study, select the appropriate statistical test to analyze the data.**b. Formulating Hypotheses** - **Null Hypothesis (\(H_0\)):** The population proportion of millionaires who can wiggle their ears is equal to 13%. \[H_0 : p = 0.13\]- **Alternative Hypothesis (\(H_1\)):** The population proportion of millionaires who can wiggle their ears is different from 13%. \[H_1 : p \neq 0.13\]**c. Calculation of Test Statistic** - Calculate the test statistic and provide the answer to three decimal places.**d. Determination of P-value** - Compute the p-value and ensure it is presented to three decimal places.**e. Comparison of P-value and Alpha** - Analyze if the p-value is less than or equal to \(\alpha\).**f. Decision Making** - Based on the p-value, decide whether to reject the null hypothesis.**g. Conclusion** - Formulate the final conclusion based on the statistical analysis: - \(\bigcirc\) The data suggest the population proportion is not significantly different from 13% at \(\alpha = 0.01\), indicating statistically insignificant evidence to conclude that the population proportion of millionaires who can wiggle their ears is different from 13%. - \(\bigcirc\) The data suggest the population proportion is not significantly different from 13% at \(\alpha = 0.01\), indicating statistically significant evidence to conclude that the population proportion of millionaires who can wiggle their ears is equal to 13%. - \(\bigcirc\) The data suggest the population proportion is significantly different from 13% at \(\alpha = 0.01

a.Suppose p is the true population proportion of millionaires who can wiggle their ears.It is needed to test whether the true population proportion of millionaires who can wiggle their ears is different from 13%. Thus, the hypothesis value of p is 0.13.In a random sample of 364 millionaires surveyed, 40 could wiggle their ears. The sample size is n = 364 and the number of successes is, x = 40. The sample proportion is, p̂ = x/n = 40/364 = 0.109890109.Now, np = (364)(0.13) = 47.32 > 5 and nq = n(1 – p) = (364)(1 – 0.13) = 316.68 > 5.That is, both the number of successes and the number of failures is at least 5.The number of observations is large (>30). The sample is selected randomly and independently.For this study we should use one sample proportion z test.b.It is needed to test whether the true population proportion of millionaires who can wiggle their ears is different from 13%.The null and alternative hypotheses are:H0: p = 0.13H1: p ≠ 0.13The test is two-tailed.c.The test statistic is:The test statistic is –1.141.d.Using the Excel formula, =NORM.S.DIST(-1.141,TRUE), it is obtained that P(z < –1.141) ≈ 0.1269.The excel output is,Thus, p-value ≈ 2PH0 (z < –1.141) = 2[0.1269] = 0.254.That is, p-value is 0.254.e.The level of significance is α = 0.01.Decision rule:If p-value is less than or equal to the level of significance, reject the null hypothesis.Otherwise, fail to reject the null hypothesis.Conclusion:The p-value is > α.f.Based on this, we should fail to reject the null hypothesis.g.The data suggest the population proportion is not significantly different from 13%, at α = 0.01, so there is statistically insignificant evidence to conclude that the population proportion of millionaires who can wiggle their ears is different from 13%.a.For this study we should use one sample proportion z test.b.The null and alternative hypotheses are:H0: p = 0.13H1: p ≠ 0.13c.The test statistic is –1.141.d.The p-value is 0.254.e.The p-value is > α.f.Based on this, we should fail to reject the null hypothesis.g.The data suggest the population proportion is not significantly different from 13%, at α = 0.01, so there is statistically insignificant evidence to conclude that the population proportion of millionaires who can wiggle their ears is different from 13%.