4. [1.74/3.5 Points] DETAILS PREVIOUS ANSWERS DEVORESTAT9 8.4.048. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER With domes

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4 1 74 3 5 Points Details Previous Answers Devorestat9 8 4 048 My Notes Ask Your Teacher Practice Another With Domes 1 (89.06 KiB) Viewed 85 times

4. [1.74/3.5 Points] DETAILS PREVIOUS ANSWERS DEVORESTAT9 8.4.048. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER With domestic sources of building supplies running low several years ago, roughly 60,000 homes were built with imported Chinese drywall. According to an article federal investigators identified a strong association between chemicals in the drywall and electrical problems, and there is also strong evidence of respiratory difficulties due to the emission of hydrogen sulfide gas. An extensive examination of 56 homes found that 44 had such problems. Suppose these 56 were randomly sampled from the population of all homes having Chinese drywall. (a) Does the data provide strong evidence for concluding that more than 50% of all homes with Chinese drywall have electrical/environmental problems? Carry out a test of hypotheses using a = 0.01. State the appropriate null and alternative hypotheses. O Ho: p = 0.5 Hip > 0.5 O Ho: p2 0.5 Hp < 0.5 O Ho: P = 0.5 Hp < 0.5 O Ho: p = 0.5 Hap < 0.5 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = 0.7857 x P-value = 0 State the conclusion in the problem context. O Do not reject the null hypothesis. There is not sufficient evidence to conclude that the true proportion of homes with problematic drywall among those with Chinese drywall is greater than 50%. Reject the null hypothesis. There is not sufficient evidence to conclude that the true proportion of homes with problematic drywall among those with Chinese drywall is greater than 50%. O Do not reject the null hypothesis. There is sufficient evidence to conclude that the true proportion of homes with problematic drywall among those with Chinese drywall is greater than 50%. Reject the null hypothesis. There is sufficient evidence to conclude that the true proportion of homes with problematic drywall among those with Chinese drywall is greater than 50%. (b) Calculate a lower confidence bound using a confidence level of 99% for the percentage of all such homes that have electrical/environmental problems. (Round your answer to one decimal place.) 73.1 X % (c) If it is actually the case that 80% of all such homes have problems, how likely is it that the test of (a) would not conclude that more than 50% do? (Round your answer to four decimal places.)