In the past, 30% of a country club's members brought guests to play golf sometime during the year. Last year, the club initiated a new program designed to encourage members to bring more guests to play golf. In a sample of 95 members, 34 brought guests to play golf after the program was initiated. When testing the hypothesis that the new program has increased the proportion of members bringing out guests (using a 5% level of significance), what is the null and alternative hypothesis?

12- The University is considering changing the email system that they currently use. Since there are substantial learning costs associated with any new software, the University only wants to change to the new system if it is very confident that there is at least a 20% difference in the proportion of faculty and staff who say they like the new system. In a sample of 134 users of the current system, the University finds that 65 say they like the current system. In another sample of 92 experimental users of the "new" system, the University finds that 75 of them like the new system. When testing the hypothesis (using a 5% level of significance) that there is at least a 20% difference in the proportion of users who like the two systems, what is the test statistic? (please round your answer to 2 decimal places)

13- The University is considering changing the email system that they currently use. Since there are substantial learning costs associated with any new software, the University only wants to change to the new system if it is very confident that there is at least a 20% difference in the proportion of faculty and staff who say they like the new system. In a sample of 120 users of the current system, the University finds that 65 say they like the current system. In another sample of 90 experimental users of the "new" system, the University finds that 70 of them like the new system. When testing the hypothesis (using a 5% level of significance) that there is at least a 20% difference in the proportion of users who like the two systems, the p-value is .2943; what is your conclusion concerning the null hypothesis?

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