A study evaluated the serum acid levels in individuals with Down's syndrome and normal individuals, the study data are shown below 2 = 1.4 1- 5.5 n1 = 12 Down's syndrome: 2= 1.6 82 = 4.3 n2 = 14 Normal individual: C = .05 Test if the mean of serum acid levels in individuals with Down's syndrome is greater than the normal individuals
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- A researcher did a one-tailed one-sample t-test to test the hypothesis that babies prefer the color blue over the color red. He collected a sample of 26 babies and presented them with a red plastic star and a blue plastic start for 12 seconds. The researcher measured the amount of time each baby spent watching the blue star out of the 12 seconds. What is the critical t value, assuming the alpha level used was .05?J 2 RCT was conducted to evaluate efficacy and safety of drug simvastatin compared to placebo in reducing mortality and morbidity in patients with coronary heart disease. Subjects were followed up on average 5.4 years. Over the duration of the follow-up, 63 subjects died due to heart attack among 2,223 subjects in the placebo group compared to 30 deaths among 2,221 patients in the simvastatin drug group. 1. What is the Relative Risk or death from the heart attack in the simvastatin group?Alexa hypothesizes that consuming whole-grain cereal for breakfast will cause students to take part in more exercise throughout the day. Assuming that she chooses an alpha level of .05, what is the critical z of her test?
- The appearance of leaf pigment glands in the seedling stage of cotton plants is genetically controlled. According to one theory of the control mechanism, the population ratio of glandular to glandless plants resulting from a certain cross should be 11.5, according to another it should be 13:3. In one experiment, the cross produced 89 glandular and 36 glandless plants. Use goodness-of-fit tests (at alpha= 0.10) to determine whether the data is consistent with a) the 11:5 theory, ar b) the 13:3 theory.A survey of 90 recently delivered women on the rolls of a county welfare department revealed that 27 had a history of intrapartum or postpartum infection. Can we conclude that the population proportion with a history of intrapartum or postpartum infection is significantly less than or equal to 0.25? Let alpha = 0.05.A survey of 90 recently delivered women on the rolls of a county welfare department revealed that 27 had a history of intrapartum or postpartum infection. What is the critical value of z if we need to conclude that the population proportion with a history of intrapartum or postpartum infection is less than 0.25.
- A nationwide study of undergraduate students reported that the mean number of drinks consumed per week during the spring semester is 7.96. The mean number of drinks consumed per week at USC is 7.64 (s.d.=2.55, N=412 Health services is concerned that USC students are consuming significantly more alcohol per week than the national average. Using an alpha level of .05, Is there sufficient evidence to be concerned? Be sure to select the correct critical value for the alternative hypothesis, and then use this evidence to make your conclusionNatalie conducted a study on the effects of triclosan on three algae populations. She collected an algae sample from three different ponds, counted the number of algae cells present in the sample, and then exposed them to a 5 ppm aqueous solution of triclosan and re-counted the number of algae cells in each sample. Using a paired t-test, she obtained a p-value of 0.083 when comparing the original algae population sizes to the population sizes after exposure to triclosan. Natalie concluded that triclosan is toxic to algae because her data for the three samples showed a trend toward a reduction in population size. What could Natalie do to show a statistically significant effect of triclosan on algae population size? Justify your response.In an observational study, it was noticed that people that eat more chocolate tend to have better blood flow than the general population. Researchers wonder whether the improved blood flow might be caused by flavanols (a molecule found in many foods). Dark chocolate contains a high concentration of flavanols, but milk chocolate contains a much lower concentration. How could the researchers design an experiment to determine the effects of flavanol on blood flow from the different types of chocolate?
- It is believed that a sweetener called xylitol helps prevent ear infections. In a randomized experiment, 165 children took a placebo and 68 of them got ear infections. Another sample of 159 children took xylitol and 46 of them got ear infections. The scientists believe that the proportion of ear infections in the placebo group will be greater than the xylitol group. Test this hypothesis at α = 0.025.HIV/AIDS patients are regularly monitored for their CD4 counts in order to make sure that antiretroviral therapies are effectiveSuppose the distribution of CD4 counts in a population is approximately normal with mu = 237 and sigma = 43 . HIV patients are defined as moving into the AIDS stage of their disease course after their CD4 counts are less than 200. What proportion of patients in this population is suffering from AIDS?A drug company maintains that a new drug G for a certain disease has a 50% cure rate as compared with drug H, which has only a 25% cure rate. You are asked to design a clinical trial comparing drugs G and H. Using the following table, estimate the number of patients needed in each therapy group to detect such a difference with alpha=0.05, two-sided, and beta=0.20.