Suppose that the results of carrying out the hypothesis test lead to non-rejection of the null hypothesis. Classify that conclusion by error type or as a correct decision if in fact the mean age at diagnosis of all people with early-onset dementia is less than 55 years old. Suppose that the manufacturer of a new COVID-19 vaccine in South Africa wants to test the null hypothesis Ho: 0= 0.90 against the alternative hypothesis H₁:0 = 0.60. She defined her test statistic Y as a number of patients recovered from COVID-19 after an observed twenty trials. If she decided to accept H, and assume y > 14, i) What will be her Type I error and the power of the test. ii) Explain how the probability of Type II error can be reduced in this case and how it will affect Type I error. Give a practical example.
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- Are freshmen psychology majors just as likely to change their major before they graduate compared to freshmen business majors? 366 of the 673 freshmen psychology majors from a recent study changed their major before they graduated and 394 of the 705 freshmen business majors changed their major before they graduated. What can be concluded at the a = 0.10 level of significance? For this study, we should use z-test for the difference between two population proportions a. The null and alternative hypotheses would be: Họ: p1 vv p2 Vv (please enter a decimal) H1: p1 p2 (Please enter a decimal) b. The test statistic z v -0.560 x (please show your answer to 3 decimal places.) c. The p-value 0.5754 (Please show your answer to 4 decimal places.) d. The p-value is >v a e. Based on this, we should fail to reject vV the null hypothesis. f. Thus, the final conclusion is that ... O The results are statistically significant at a = 0.10, so there is sufficient evidence to conclude that the proportion…Are freshmen psychology majors just as likely to change their major before they graduate compared to freshmen business majors? 366 of the 673 freshmen psychology majors from a recent study changed their major before they graduated and 394 of the 705 freshmen business majors changed their major before they graduated. What can be concluded at the a = 0.10 level of significance? For this study, we should use z-test for the difference between two population proportions a. The null and alternative hypotheses would be: Ho: p1 p2 v (please enter a decimal) H1: p1 p2 (Please enter a decimal) b. The test statistic z v -0.508 X (please show your answer to 3 decimal places.) c. The p-value = 0.6115 X (Please show your answer to 4 decimal places.) d. The p-value is > vV a e. Based on this, we should fail to reject the null hypothesis. f. Thus, the final conclusion is that ... O The results are statistically significant at a = 0.10, so there is sufficient evidence to conclude that the proportion of…A researcher has observed 500 vehicles at a stop in a suburban neighborhood and recorded the type of vehicle (sedan, hatchback, bakkie) and driver behavior ar the stop sign (complete stop, near stop, "ran" tha stop sign). At the 0.05 level of significance, could there be some relationship between driver behavior and the type of vehicle being driven? Define the null hypothesis and the alternative hypothesis.
- A mutation in Gene A is thought to be associated with a disease. The mutation in Gene A is found in 5% of the population. 2% of the whole population is diagnosed with disease B at some point in their life time. 1% of the population both has the mutation and also gets diagnosed with the disease in their life time. Is the provided data adequate to test the independency of mutation in Gene A and occurrence of Disease B? If it is not, what other information or data is needed to test the independency? What is the probability of Disease B, among the individuals with the mutation in Gene A? What is the probability of having the mutation in Gene A among the individuals with Disease B? If an individual has the mutated Gene A, what is their Relative Risk of developing the disease?A researcher states an alternative hypothesis that the exercise improves physical health. Which is a possible null hypothesis corresponding to this alternative hypothesis? Exercise worsens physical health Physical health is not impacted by exercises Exercises worsens or has no impact on physical healthA doctor believes that the fruit and vegetable intake of Northern adolescents is different from the fruit and vegetable intake of Southern adolescents. To study this, she gathers data on the number of fruits and vegetables eaten per week from a random sample of Northern adolescents and a random sample of Southern adolescents. Which is an appropriate null hypothesis for the study? The average number of fruits and vegetables eaten per week among Northern adolescents is less than the average number of fruits and vegetables eaten per week among Southern adolescents. The average number of fruits and vegetables eaten per week among Northern adolescents is the same as the average number of fruits and vegetables eaten per week among Southern adolescents. The average number of fruits and vegetables eaten per week among Northern adolescents is greater than the average number of fruits and vegetables eaten per week among Southern adolescents. The average number of fruits and vegetables eaten per…
- A comprehensive trial investigating the relationship between vitamin E supplementation and reduced risk for prostate cancer was carried out across the US. Suppose the trial reported that among the 648 patients receiving the supplement program, 267 developed prostate cancer, while only 212 of the 711 patients without the supplementation developed the disease. Carry out a formal test to determine if there is a significant difference in the risk for developing prostate cancer among the two groups. Write out your null and alternative hypotheses and use an alpha level of 0.05. Also, Comment on the effectiveness of the supplementation at reducing prostate cancer. What did you find relevant to the research hypothesis?A car leasing firm's records indicate that the mean number of miles driven annually in its cars has been about 17,500 miles. The firm suspects that this number has decreased this past year. Suppose that the firm wishes to choose a small sample of driving distances from the past year and carry out a hypothesis test for its suspicion. State the null hypothesis H0 and the alternative hypothesis H1 that it would use for this test.Consider a proposed case-control study of autism spectrum disorder (ASD) and maternal boba tea consumption in Irvine. Assume that 20% of Irvine mothers are regular consumers (at least 3 servings per week) of boba tea, and that the prevalence of ASD is 1/59 (making it a somewhat rare disease). Also assume that 50% of Irvine mothers who regularly consume boba tea prefer black milk tea, that the prevalence of regular boba tea consumption among mothers of autistic children is 25%, that each participant will be paid $30 to join the study, and that there are at least 1,000 mothers of autistic children and at least 100,000 mothers of non-autistic children in Irvine who are willing to participate in the study if compensated. If these assumptions are correct, what is the odds ratio describing the association between regular boba tea consumption and ASD? HINT: Recall that the disease odds ratio is equal to the exposure odds ratio.
- A researcher wants to determine if there is a significant difference in the number of times a new treatment for a medical condition results in relief from symptoms compared to the standard treatment. They randomly assign 20 patients to receive the new treatment and 20 to receive the standard treatment, and record the number of times each patient experienced relief from symptoms in a given period of time. The researcher uses the Wilcoxon Signed-Ranks Test to analyze the data. What is the null hypothesis for this test?Suppose a professional basketball player historically makes 37% of his three-point field goals. After a rigorous off-season training, the -player makes 36 of his 75 three-point field goals Does this represent significant evidence that the player's three-point field goal shooting has ?improved What is your decision about the null hypothesis, ?consider a = 0.05? Why We reject the null hypothesis at a = 0.05 . Zo > z0.025 significance level, because We reject the null hypothesis at a = 0.05 to > to.025 significance level, because We fail to reject the null hypothesis at a = 0.05 .-Z0.05 < z0 < z0.05 significance level, because We fail to reject the null hypothesis at a = 0.05 --Z0.025 < zo < z0.025 significance level, becauseA 2012 survey of 417 American adults indicates that 15% of cell phone owners do their browsing on their phone rather than a computer or other device. According to an online article, a report from a mobile research company indicates that 38% of Chinese mobile web users only access the internet through their cell phones. We wish to conduct a hypothesis test to determine if these data provide strong evidence that the proportion of Americans who only use their cell phones to access the internet is less than the Chinese proportion of 38%. (a) The Null Hypothesis, in mathematical symbols, is: H0: p = ______ (b) The Alternative Hypothesis, in mathematical symbols, is: HA : p = _______ In both the null and alternative hypotheses, the symbol ( p ) is the proportion of American adult cell phone owners who do their browsing on their phone. (c) The standard error based on the null hypothesis is... :________ (d) Our data indicates a proportion of Americans who use their phones to browse is…