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An article included data from a survey of 188 senior managers in a range of industries In this sample only 28 managers reported that their meetings are generally productive uses of group and individual time USE SALT a Do these data provide convincing evidence that fewer than one quarter of all senior managers in the United States believe that their meetings are generally productive Use the five step process for hypothesis testing HMC described in this section and a 0 05 to test the appropriate hypotheses You may assume that the sample is representative of all senior managers in the United States State the appropriate null and alternative hypotheses Let p be the population proportion of all senior managers in the United States who believe that their meetings are generally productive Enter for as needed Ho H Find the test statistic Round your answer to two decimal places Use technology to find the P value Round your answer to four decimal places P value State the conclusion in the problem context Fail to reject Ho We do not have convincing evidence that fewer than one quarter of all senior managers in the United States believe that their meetings are generally productive Reject Ho We do not have convincing evidence that fewer than one quarter of all senior managers in the United States believe that their meetings are generally productive Reject Ho We have convincing evidence that fewer than one quarter of all senior managers in the United States believe that their meetings are generally productive O Fail to reject Ho We have convincing evidence that fewer than one quarter of all senior managers in the United States believe that their meetings are generally productive b Based on the results of the hypothesis test is it appropriate to conclude that the proportion of all senior managers in the United States who believe their meetings are generally productive is a lot less than 0 25 OYes Since the hypothesis test rejected the null hypothesis we can definitively conclude that that the proportion of all senior managers in the United States who believe their meetings are generally productive is a lot less than 0 25 that the proportion of all senior managers in the United States who believe their meetings

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