10.5 The table summarizes the outcomes of a study that students carried out to determine whether humanities students had a higher mean grade point average (GPA) than science students. Identify both of the variables, and state whether they are numerical or categorical. If numerical, state whether they are continuous or discrete. Science Humanities Mean GPA 3.4 3.5
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- Globally, 35% of all ridged brittleshell tortoises have spots on their shells. A herpetologist in Citition collects a sample of 38 ridged brittlesell tortoises and finds that 16 of them have spots on their shells. The herpetologist would like to test the claim that the proportion of ridged brittleshell tortoises in Cititon with spots on their shells is greater than 35%. The herpetologist ends up rejecting the null hypothesis. If the actual proportion of ridged brittleshell tortoises in Cititon with spots on their shells is 41%, then what type of error, if any, has occurred? In the problem above, what is the test statistic?Suppose that 80% of 3–4-year-old children and 70% of5–8-year-old children in a village are vaccinated with QIVvaccine. Also assume that children who are not vaccinatedhave twice the incidence of influenza as the control groupin Table 3.7.3.29 What % of 3–4-year-old children in the village will getinfluenza?3.30 What % of 5–8-year-old children in the village will getinfluenza?3.31 Suppose we identify a 5–8-year-old child with influenzain the village but are uncertain whether the childwas vaccinated. If we make the same assumptions as inProblems 3.29–3.30, then what is the probability that thechild was vaccinated? (Hint: Use Bayes’ rule here.)A researcher wonders if there an association between the incidence of colds and the amount of vitamin C taken. He recruits 98 volunteers and randomly assigns 29 of them to take 500 mg of vitamin C, 17 of them to take 1000 mg of vitamin C and the rest to take no vitamin C. At the end of the study, it was determined that 28 of the volunteers did not have any colds where 12 of them were in the 500 mg group and 8 of them were in the 1000 mg group. Test the appropriate hypothesis at α=.01 Complete the table of expected counts under the null hypothesis. At least one cold No colds No vitamin C 14.857 500 mg vitamin C 20.714 1000 mg vitamin C 12.143 4.857
- A survey of states found that the proportions of achults who are smokers in Alabama was 24.8% and in Missouri it was 23.4%Both samples had 2000 people. At alpha = 0.01 the researchers claim that the proportion of adults who are smokers is greater in Alabama than in Missouri What is the correct set of hypotheses for this scenario ?A researcher wonders if there an association between the incidence of colds and the amount of vitamin C taken. He recruits 86 volunteers and randomly assigns 25 of them to take 500 mg of vitamin C, 19 of them to take 1000 mg of vitamin C and the rest to take no vitamin C. At the end of the study, it was determined that 26 of the volunteers did not have any colds where 12 of them were in the 500 mg group and 9 of them were in the 1000 mg group. Test the appropriate hypothesis at α=.05.α=.05. Round all answers to three decimal places. (a). H0:H0: There Select an answer is is not an association between the incidence of colds and the amount of vitamin C taken. (b). Ha:Ha: There Select an answer is is not an association between the incidence of colds and the amount of vitamin C taken. (c). Complete the table of expected counts under the null hypothesis. Hint At least one cold No colds No vitamin C 12.698 500 mg vitamin C 17.442 1000 mg vitamin C 13.256 5.744…A seven-year medical research study reported that women whose mothers took the drug DES during pregnancy were twice as likely to develop tissue abnormalities that might lead to cancer as were women whose mothers did not take the drug. a. This study compared two What were the populations? b. Do you suppose the data were obtained in a survey or an experiment? c. For the population of women whose mothers took the drug DES during pregnancy, a sample of 3980 women showed that 63 developed tissue abnormalities that might lead to Provide a descriptive statistic that could be used to estimate the number of women out of 1000 in this population who have tissue abnormalities. d. For the population of women whose mothers did not take the drug DES during pregnancy, what is the estimate of the number of women out of 1000 who would be expected to have tissue abnormalities? e. Medical studies often use a relatively large sample (in this case.3980).Why?
- A seven-year medical research study reported that women whose mothers took the drugDES during pregnancy were twice as likely to develop tissue abnormalities that might leadto cancer as were women whose mothers did not take the drug.a. This study compared two populations. What were the populations?b. Do you suppose the data were obtained in a survey or an experiment?c. For the population of women whose mothers took the drug DES during pregnancy, asample of 3980 women showed that 63 developed tissue abnormalities that might leadto cancer. Provide a descriptive statistic that could be used to estimate the number ofwomen out of 1000 in this population who have tissue abnormalities.d. For the population of women whose mothers did not take the drug DES duringpregnancy, what is the estimate of the number of women out of 1000 who would beexpected to have tissue abnormalities?A seven-year medical research study reported that women whose mothers took the drugDES during pregnancy were twice as likely to develop tissue abnormalities that might leadto cancer as were women whose mothers did not take the drug.a. This study compared two populations. What were the populations?b. Do you suppose the data were obtained in a survey or an experiment?c. For the population of women whose mothers took the drug DES during pregnancy, asample of 3980 women showed that 63 developed tissue abnormalities that might leadto cancer. Provide a descriptive statistic that could be used to estimate the number ofwomen out of 1000 in this population who have tissue abnormalities2. A leading researcher in the study of interstate highway accidents proposes that a major cause of many collisions on the interstates is not the speed of the vehicles but rather the difference in speeds of the vehicles. When some vehicles are traveling slowly while other vehicles are traveling at speeds greatly in excess of the speed limit, the faster-moving vehicles may have to change lanes quickly, which can increase the chance of an accident. Thus, when there is a large variation in the speeds of the vehicles in a given location on the interstate, there may be a larger number of accidents than when the traffic is moving at a more uniform speed. The researcher believes that when the standard deviation in speed of vehicles exceeds 10 mph, the rate of accidents is greatly increased. During a 1-hour period of time, a random sample of 50 vehicles is selected from a section of an interstate known to have a high rate of accidents, and their speeds are recorded using a radar gun. The data…
- Suppose a fertilizer company wants to test the effectiveness of a new fertilizer on its corn fields. The company divides a corn field into rectangular patches of the same area and randomly selects certain patches to which the fertilizer is applied and other patches to which no fertilizer is applied. The patches to which no fertilizer is applied serves as a *fill in the blank* for the experiment. (i) control (ii) placebo (iii) observation (iv) non-treatmentA graduate student realized that the depression study above in Question 4 should have had a placebo condition in which a third group was given a pill just as the people in the Drug condition were, but where the pill was not Drug D (e.g., a sugar pill). So she designed a new experiment with three conditions -- Drug, No Drug, and Placebo. To perform the experiment, the graduate student randomly assigned 18 people into the three groups so that each group has 6 people. After one month of treatment, all 18 people were asked to rate on a scale from 1 to 7 how depressed they felt, where 1 = not depressed at all and 7 = very depressed. The following are the data: Drug No Drug Placebo 2 4 5 3 5 5 4 5 6 4 4 5 2 6 4 3 6 5 nD = 6 nND = 6 nplacebo = 6 MD = 3 MND = 5 Mplacebo = 5 Using an α-level of .05, perform an…The National Institute of Mental Health published an article stating that in any two-year period, approximately 10.5percent of American adults suffer from depression or a depressive illness. Suppose that in a survey of 150 people in a certain town, eight of them suffered from depression or a depressive illness. If you were conducting a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population, what would the null and alternative hypotheses be?