A major restaurantchain created a poll which showed the following statements to respondents (statements were in random order per respondent) Servicestatement: The most important part of a restaurantvisit is thequality of the service. Food Statement: The most important part of a restaurant visit is the quality of the food. Thesurveywas given toa random sample of 512 USadults. After readingthestatement, the person being polled chose the statement they agreed with the most. Here are the results: PercentofSam le Service Statement Food Statement 52% No Preference 5% b. Assume theconditionsfor inference have been met. Constructa 95% confidence intervalfor the proportion of all adults in the U nited States who would have chosen the Service Statement. One of the conditions for inference to be met is that the number of respondents who chose the Service Statement and the number who chose the Food Statement are both greater than 10. Explain why it is necessarytofulfill this condition. We are thinking of usinga two-sample z-intervalfor a difference between proportions to investigate whether the difference in proportions between adults in the US who would have chosen the Service Statement and adults in the US who would have chosen the food statement is statistically significant. Is thetwo samplez-intervalfor a difference between proportionsthe an appropriate procedure to investigate the difference?