A well-known brokerage firm executive claimed that 90% of investors are currently confident of meeting their investment goals. An XYZ Investor Optimism Survey, conducted over a two week period, found that in a sample of 200 people, 98% of them said they are confident of meeting their goals: Test the claim that the proportion of people who are confident is larger than 90% at the 0.005 significance level. The null and alternative hypothesis would be: Ho:p = 0.9 Ho:u = 0.9 Ho:p 2 0.9 Ho:u 2 0.9 Ho:µ <0.9 Ho:p< 0.9 H1:p 0.9 H1: 0.9 H1:p < 0.9 H1:u < 0.9 H1:p > 0.9 H1:p > 0.9 %3D %3D The test is: two-tailed left-tailed right-tailed The test statistic'is: (to 3 decimals) The p-value is: (to 4 decimals) Based on this we: O Fail to reject the null hypothesis O Reject the null hypothesis

6. In the past, 70% of a garage's business was with former patrons. Clarence Wade, the owner of the garage, samples 600 repair invoices and finds that for 432 of them, the patron was a repeat customer. a. Develop a 90% confidence interval for the proportion of all current business that is with repeat customers.

A survey asked senior executives at large corporations their opinions about the economic outlook for the future. One question was, "Do you think that there will be an increase in the number of full- time employees at your company over the next 12 months?" In the current survey, 232 of 400 executives answered Yes, while in a previous year survey, 184 of 400 executives had answered Yes. Provide a 95% confidence interval estimate for the difference between the proportions at the two points in time. (Use current year previous year. Round your answer to four decimal places.) to What is your interpretation of the interval estimate? The 95% confidence interval ---Select--- ✓zero. This suggests that the proportion of executives who are predicting an increase in full-time jobs for the current year is ---Select---] than the proportion of executives who were predicting an increase in full-time jobs for the previous year.

A study regarding the proportion of students who finish their MS degree (graduate) is conducted in two universities (A and B). The results are shown in the following table.