Suppose that a criterion for vitamin D deficiency is a serum 25-OHD level that is 1.2 standard deviations below the mean of healthy adults. Lifeguards are not ‘typical’ healthy adults since they experience much higher sun exposure. As a result, the mean serum 25-OHD for lifeguards is about +3 on the standard scale for healthy adults. Suppose that the standard deviation is the same as for healthy adults. What percent of lifeguards have vitamin D deficiency?
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- A psychologist is studying the self image of smokers, as measured by the self-image (SI) score from a personality inventory. She would like to examine the mean SI score, μ, for the population of all smokers. Previously published studies have indicated that the mean SI score for the population of all smokers is 85 and that the standard deviation is 15, but the psychologist has good reason to believe that the value for the mean has changed. She plans to perform a statistical test. She takes a random sample of SI scores for smokers and computes the sample mean to be 75. Based on this information, complete the parts below. (a) What are the null hypothesis Ho and the alternative hypothesis H₁ that should be used for the test? μ x H₁ : ☐ H₁:0 □<ロ □ㄨˇ OA researcher studying stress is interested in the blood pressure measurements of chief executive officers (CEOs) of major corporations. He has good reason to believe that the mean systolic blood pressure, μ, of CEOs of major corporations is different from 132 mm Hg, which is the value reported in a possibly outdated journal article. He plans to perform a statistical test. He measures the systolic blood pressures of a random sample of CEOs of major corporations and finds the mean of the sample to be 124 mm Hg and the standard deviation of the sample to be 20 mm Hg. Based on this information, complete the parts below. A. H0: H1: B. Suppose that the researcher decides to reject the null hypothesis. Would the research be making a type I or type II error?In nutrition, the recommended daily allowance of vitamins is a number set by the government to guide an individual's daily vitamin intake. Actually, vitamin needs vary drastically from person to person, but the needs are closely approximated by a normal curve. To calculate the recommended daily allowance, the government first finds the standard deviation and the average need for vitamins among people in the population. The recommended daily allowance is then defined as the mean plus 2.7 times the standard deviation. What fraction of the population will receive adequate amounts of vitamins under this plan? Click here to see page 1 of the table for areas under the standard normal curve. Click here to see page 2 of the table for areas under the standard normal curve. The fraction of the population that will receive adequate amounts of vitamins under the given plan is (Type an integer or decimal rounded to the nearest thousandth as needed.)A psychologist is studying the self image of smokers, as measured by the self-image (SI) score from a personality inventory. She would like to examine the mean SI score, μ, for the population of all smokers. Previously published studies have indicated that the mean SI score for the population of all smokers is 82and that the standard deviation is 12, but the psychologist believes that the value for the mean has decreased. She plans to perform a statistical test. She takes a random sample of SI scores for smokers and computes the sample mean to be 7.Based on this information, answer the questions below. What are the null hypothesis (H0) and the alternative hypothesis (H1) that should be used for the test?H0: μ is ?less than less than or equal togreater thangreater than or equal to not equal toequal to ? 82 74 12 H1: μ is ?less thanless than or equal togreater thangreater than or equal tonot equal toequal to ? 82 74 12 In the context of this test, what is a Type II error?A Type…A psychologist is studying the self image of smokers, as measured by the self-image (SI) score from a personality inventory. She would like to examine the mean SI score, μ , for the population of all smokers. Previously published studies have indicated that the mean SI score for the population of all smokers is 80 and that the standard deviation is 12 , but the psychologist believes that the value for the mean has decreased. She plans to perform a statistical test. She takes a random sample of SI scores for smokers and computes the sample mean to be 74 . Based on this information, answer the questions below. What are the null hypothesis ( H0 ) and the alternative hypothesis ( H1 ) that should be used for the test? H0 : μ is ?less thanless than or equal togreater thangreater than or equal tonot equal toequal to ?748012 H1 : μ is ?less thanless than or equal togreater thangreater than or equal tonot equal toequal to ?748012In the…Reports on a student's test score such as the SAT or a child's height or weight usually give the percentile as well as the actual value of the variable. The percentile is just the cumulative proportion stated as a percent: the percent of all values of the variable that were lower than this one. The upper arm lengths of females in the United States are approximately Normal with mean 35.735.7 cm and standard deviation 2.12.1 cm, and those for males are approximately Normal with mean 39.139.1 and standard deviation 2.32.3 cm. Larry, a 6060‑year‑old male in the United States, has a upper arm length of 37.837.8 cm. What is his percentile? (Enter your answer rounded to two decimal places.)The mean score for first exam in your first organic chemistry class (section A) was 60, with a standard deviation of 5. Your score on the exam was 70. A. How many standard deviations above the mean is your score?Two chemical companies can supply a raw material. The concentration of a particular element in this material is important. The mean concentration for both suppliers is the same, but you suspect that the variability in concentration may differ for the two companies. The standard deviation of concentration in a random sample of n₁ = 10 batches produced by company 1 is s₁ = 4.7 grams per liter, and for company 2, a random sample of n₂ = 16 batches yield s₂ = 5.8 grams per liter. Is there sufficient evidence to conclude that the two populations variances differ? Use a = 0.05. a. Because 0.321 < 0.657 <3.77, fail to reject the null hypothesis b. Because 0.265 < 0.657 <3.12, fail to reject the null hypothesis c. Because 0.386 < 0.657 <3.01, fail to reject the null hypothesis d. None among the choicesA researcher studying stress is interested in the blood pressure measurements of chief executive officers (CEOs) of major corporations. He has good reason to believe that the mean systolic blood pressure, μ, of CEOs of major corporations is different from 132 mm Hg, which is the value reported in a possibly outdated journal article. He plans to perform a statistical test. He measures the systolic blood pressures of a random sample of CEOs of major corporations and finds the mean of the sample to be 124 mm Hg and the standard deviation of the sample to be 20 mm Hg. Based on this information, complete the parts below. Suppose the true mean systolic blood pressure of CEOs of major corporations is 132 mm Hg. Fill in the four blanks to describe a Type I error. 1. A Type I error would be (rejecting) or (failing to reject) the hypothesis 2. that μ is (less than) (less than or = to) (greater than) (greater than or = to) (not = to) or (= to) 3. the number (124) (132) or (20)…Suppose the distribution of heights of a group of 300 children is normal, with a mean of 150 centimeters and a standard deviation of 12 centimeters. About how many of these children are taller than 162 centimeters? childrenA psychologist is studying the self image of smokers, as measured by the self-image (SI) score from a personality inventory. She would like to examine the mean SI score, µ, for the population of all smokers. Previously published studies have indicated that the mean SI score for the population of all smokers is 80 and that the standard deviation is 15, but the psychologist has good reason to believe that the value for the mean has changed. She plans to perform a statistical test. She takes a random sample of SI scores for smokers and computes the sample mean to be 88. Based on this information, complete the parts below. (a) What are the null hypothesis H. and the alternative hypothesis H₁ that should be used for the test? Ho : H₁ :0 (b) Suppose that the psychologist decides not to reject the null hypothesis. What sort of error might she be making? Type I Suppose the true mean SI score for all smokers is 80. Fill in the blanks to describe a Type I error. the hypothesis that u is (Choose…Low-density lipoprotein, or LDL, is the main source of cholesterol buildup and blockage in the arteries. This is why LDL is known as "bad cholesterol." LDL is measured in milligrams per deciliter of blood, or mg/dL. In a population of adults at risk for cardiovascular problems, the distribution of LDL levels is normal, with a mean of 123 mg/dL and a standard deviation of 41 mg/dL. If an individual's LDL is at least 1 standard deviation or more above the mean, he or she will be monitored carefully by a doctor. What percentage of individuals from this population will have LDL levels 1 or more standard deviations above the mean? Use the 68–95–99.7 rule. (Enter your exact answer as a whole number.) percentage %
