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In an investigation of the personality characteristics of drug dealers of a certain region, convicted drug dealers were scored on a scale that provides a quantitative measure of a person's level of need for approval and sensitivity to social situations. (Higher scores indicate a greater need for approval.) Based on the study results, it can be assumed that the scale scores for the population of convicted drug dealers of the region has a mean of 42 and a standard deviation of 7. Suppose that in a sample of 88 people from the region, the mean scale score is x = 44. Is this sample likely to have been selected from the population of convicted drug dealers of the region? Explain. Consider an event with a probability less than 0.05 unlikely. Select the correct choice below and fill in the answer box within your choice. (Round to four decimal places as needed.) () A. Yes, because the probability that a randomly selected sample of convicted drug dealers of the region has a sample mean of 44 or greater is which is greater than 0.05. () B. No, because the probability that a randomly selected sample of convicted drug dealers of the region has a sample mean of 44 or less is which is greater than 0.05. () C. No, because the probability that a randomly selected sample of convicted drug dealers of the region has a sample mean of 44 or greater is which is less than 0.05. According to a poll of adults, about 50% work during their summer vacation. Assume that the true proportion of all adults that work during summer vacation is p =0.50. Now consider a random sample of 400 adults. Complete parts a and b below. a. What is the probability that between 43% and 57% of the sampled adults work during summer vacation? The probability is D (Round to three decimal places as needed.) b. What is the probability that over 66% of the sampled adults work during summer vacation? The probability is | |. (Round to three decimal places as needed.) A random sample of n =81 observations is drawn from a population with a mean equal to 24 and a standard deviation equal to 18. Complete parts a through g below. a. Give the mean and standard deviation of the (repeated) sampling distribution X. B; = U)'( = (Type integers or decimals.) b. Describe the shape of the sampling distribution of x. Does this answer depend on the sample size? Choose the correct answer below. () A. The shape is that of a normal distribution and does not depend on the sample size. () B. The shape is that of a uniform distribution and does not depend on the sample size. () C. The shape is that of a normal distribution and depends on the sample size. () D. The shape is that of a uniform distribution and depends on the sample size. c. Calculate the standard normal z-score corresponding to a value of x=23.4. z= (Type an integer or a decimal.) d. Calculate the standard normal z-score corresponding to a value of x = 24 4. z= (Type an integer or a decimal.) e. Find P (x24.4). P (::_( >24.4) =| | (Round to four decimal places as needed.) \fDue to the popularity of instant messaging and social networking, informal elements such as emoticons (e.g., the symbol ":)" to represent a smile) and abbreviations (e.g., "LOL" for "laughing out loud") have worked their way into teenagers' school writing assignments. A survey interviewed 900 randomly selected teenagers by telephone on their writing habits. Overall, 439 of the teenagers admitted using at least one informal element in school writing assignments. Based on the survey results, construct a 99% confidence interval for the proportion of all teenagers who have used at least one informal element in school writing assignments. Give a practical interpretation of the interval. The 99% confidence intervalis (| |,| |). (Round to three decimal places as needed.) Interpret the interval. Choose the correct answer below. () A. One can be 1% confident that the interval contains the sample population proportion of all teenagers who have used at least one informal element in school writing assignments. (1) B. One can be 99% confident that the interval contains the sample population proportion of all teenagers who have used at least one informal element in school writing assignments. One can be 1% confident that the interval contains the true population proportion of all teenagers who have used at least one informal element in school writing assignments. One can be 99% confident that the interval contains the true population proportion of all teenagers who have used at least one informal element in school writing assignments. Health care workers who use latex gloves with glove powder on a daily basis are particularly susceptible to developing a latex allergy. Each in a sample of 46 hospital employees who were diagnosed with a latex allergy based on a skin-prick test reported on their exposure to latex gloves. Summary statistics for the number of latex gloves used per week are x = 19.5 and s = 12.3. Complete parts (a) (d). a. Give a point estimate for the average number of latex gloves used per week by all health care workers with a latex allergy. b. Form a 95% confidence interval for the average number of latex gloves used per week by all health care workers with a latex allergy. (LD (Use integers or decimals for any numbers in the expression. Round to two decimal places as needed.) c. Give a practical interpretation of the interval. part (b). (_) A. One can be 95% confident that the average number of latex gloves used per week by all healthcare workers with a latex allergy is less than the lower boundary of the interval. (1) B. One can be 95% confident that the average number of latex gloves used per week by all healthcare workers with a latex allergy is in the interval. () C. One can be 95% confident that latex gloves cause allergies for all who use a number of gloves contained in the interval. (_) D. One can be 95% confident that the average number of latex gloves used per week by all healthcare workers with a latex allergy is greater than the upper boundary of the interval. d. Give conditions required for the interval, part (b), to be valid. O A. i. The sample selected was specifically selected from the target population. ii. The sample size is sufficiently large, that is, n > 1000 O B. i. The sample selected was randomly selected from the target population. ii. The sample size is sufficiently large, that is, n > 1000 O C. i. The sample selected was randomly selected from the target population. ii. The sample size is sufficiently large, that is, n > 30 O D. i. The sample selected was specifically selected from the target population. ii. The sample size is sufficiently large, that is, n > 30