(e)Suppose that you want to estimate what percent of consumers enjoy eating cereal as a nighttime snack. How large of a sample would you need to take to obtain a margin of error of only 5% at the 95% confidence level?18.You work for a large bank. Historically, 20% of homebuyers go to a mortgage broker to apply for a mortgage rather than dealing directly with a bank. You believe that because people are becoming more financially sophisticated, the percentage of homebuyers who use a mortgage broker has increased. You take a random sample of 400 recent homebuyers and found that 100 of them used a mortgage broker. (a)Test at the 3% level of significance if their sufficient evidence to confirm your belief.(b)If H0is true, find the probability of getting a value as large or larger than 100 out of 400. (c)What does the probability in part b) represent?19.A soft drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of soft drink. random sample of 23 bottles is selected, and the contents are measured. The sample yielded a mean content of 11.80 ounces, with a standard deviation of 0.50 ounces. Assume that the amount of soft drink dispensed is normally distributed.(a)At the 10% level of significance can you conclude that the machine is not in perfect adjustment? (b)Estimatethe p-value.20.A local utility has received numerous complaints after installing new “intelligent meters”. Many customers have complained that the new meters give higher readings than old electromagnetic meters. A sample of 16 hydro bills was sampled and the difference between January 2010 and January 2011 is shown below. (January 2011 bill – January 2010 bill). Assume that hydro rates did not change and the difference between bills assumes a normal distribution.5.00$ 3.00-$ 12.00$ 2.00-$ 6.00$ 1.00-$ 25.00$ 10.004.00-$ 6.00$ 8.00$ 5.00$ 9.00$ 2.00-$ 10.00$ (a)At the 2.5% significance level is there enough evidence to conclude the new readings generate higher bills? (test 2.19, CV 2.13 reject Ho)(b)Estimate the p-value. (between 1% and 2.5%)21.Consumer Report has become aware that all the glowing reports about the reliability of the Novo Motor Company’s Juniper model may be overstated. Consumer Report has paid for a statistical study to estimate the proportion of Juniper’s cars requiring major warranty repairs. Consumer Report takes a random sample of 100 of Juniper’s 2-year old cars and finds that 9 of them required major warranty repair. (a)Construct a 95% confidence interval for the true percentageof Juniper models requiring major warranty repairs. (b)Novo’s management is very concerned about this percentage and decides to have an independent research agency do a much larger sample to be 95% confident that the error on the estimate is at most 1%. How large of a sample do they need? (c)What would your answer have been if you had not known the results of your sample of 100 Juniper cars?22.The customer service department of Max Financial Services would like to estimate the average length of time between the receipt of a customer's application for conducting on-line financial transactions and the A -$ 8.00$

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