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# CONSIDER ALL THE POSSIBLE VALUES FOR THE RESULTING SAMPLE

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Author: Christine Farr
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Question 1 Background :Bachelor's Degree Education RateEducation Rate - According to the Department of Education, 32% of adults over the age of 25 in theUnited States have earned at least a bachelor’s degree. Suppose this is the true proportion of all adultsover the age of 25 that have earned at least a bachelor’s degree. A random sample of 200 adults overthe age of 25 will be selected and their highest degree will be recorded. Let pp represent the proportionof adults over the age of 25 in the sample who have earned at least a bachelor’s degree.Question 1 SubquestionsConsider all the possible values for the resulting sample proportion pp. What is the expected value (oraverage) of all such values of pp ?32640.32unknown since we have not yet taken an actual random sample yetConsider all the possible values for the resulting sample proportion pp. What is the standard deviation ofall such values of pp ?0.0010880.032986.596969unknown since we have not yet taken an actual random sample yetPerform the check regarding the sample size that confirms the sampling distribution of the possiblevalues for pp will be approximately normally distributed. Question 2 Background :Estimating Proportion of Coffee DrinkersIn a recent survey of 150 students at a community college, 86 students said they were “regular” coffeedrinkers. Based on these results, the 95% confidence interval to estimate the population proportion ofall such college students who drink coffee regularly was found to be: 0.573 ± 0.079 or 0.494 to 0.652.Which of the following correspond to the value of 0.573?the sample proportionthe population proportionthe margin of errorthe confidence levelWhich of the following correspond to the value of 0.079?the sample proportionthe population proportionthe margin of errorthe confidence levelBased on this reported confidence interval, does there appear to be significant evidence (at a 95%confidence level) to conclude there is a majority of regular coffee drinkers in the community collegepopulation? Select the answer with the appropriate explanation.Yes, because 57.3% is above 50%.Yes, because 95% is above 50%.No, because the interval of reasonable values dips below 50%.No, because 0.079 is below 50%. Question 3 Background :In-State University?Based on a random sample of 1,250 college students, a 95% confidence interval for the populationproportion of all college students who attend an in-state university was reported as 66% to 72%.Determine whether each of the following statements is an appropriate statement that could be includedin the report summarizing these results.With 95% confidence we estimate the population proportion of all college students who attend an instate university is between 0.66 and 0.72.

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