A consumer magazine polls cell-phone-users to see if they are happy with their phones and would purchase the same model again. They randomly selected cell-phone-users and found the following: 429 of 550 owners of iPhones would purchase their phone again, and 324 of 450 owners of Androids would purchase the same phone again. a) Conduct a hypothesis test with an alpha-level of 0.05 to determine if there is strong evidence that owners of iPhones are happier with their purchase than owners of Androids. Be sure to give the name of the test that you are performing . b) If your conclusion was wrong, what type of error occurred, Type I or Type II ?

A new drug is tested in two peer-reviewed studies, A and B. Both studies provide evidence that the new drug is an improvement (The null hypothesis, that the new drug does not help, is rejected). But the researchers who conducted study A report a p-value of 8.2%, the team from study B obtained a p-value of only 2.3%. Which study provides the stronger evidence in favor of the new drug? Choose the most appropriate answer.  a. Study B, because follow-up studies usually provide stronger evidence. b. Study A, because their p-value is bigger. c. Study A, because it was done by real researchers, and B only by a 'team'. d. Study B, because their p-value is smaller. e. The evidence from both studies is too weak.

In a clinical trial to test whether a medication lowers cholesterol levels in the blood, it was given to two groups. The first group took the medication and 203 out of 350 adults showed a lower level in cholesterol levels, the second group (the control group) took a placebo and 102 out of 250 adults resulted with lower cholesterol level. Is there sufficient evidence to support this new medication lowers cholesterol levels? Show all your work and enter the test-statistic. show formulas and draw all curves.

In the past 10 years, the prevalence of peanut allergies has doubled in Western countries. Is consumption or avoidance of peanuts in infants related to the development of peanut allergies in infants at risk? Subjects included infants between four and 11 months with severe eczema, egg allergy, or both but who did not display a preexisting sensitivity to peanuts based on a skin-prick test. The infants were randomly assigned to either a treatment that avoided consuming peanut protein or a treatment in which at least 6 grams of peanut protein were consumed per week. The response was the presence or absence of peanut allergy at 60 months of age. In the avoidance group containing 263 infants, 36 had developed a peanut allergy at 60 months of age, while in the consumption group containing 266 infants, five had developed a peanut allergy. George Du Toit et al., "Randomized trial of peanut consumption in infants at risk for peanut allergy," New England Journal of Medicine, 372 (2015), pp.…

A study was conducted that investigated the gene ACTN3, which encodes a protein that functions in fast-twitch muscle fibres. People can be classified according to which genotype of this gene they have, RR, RX or XX. The study included a sample of elite sprinters and a sample of endurance athletes. The researchers are investigating whether there is an association between the genotype classification and the type of athlete (sprinters or endurance). What type of hypothesis test would be appropriate for this study? Explain your answer in one or two sentences.

An advertising agency collected a random sample of 300 businesses targeted with an advertising campaign for a large commercial bank. The sample was used to investigate the efficacy of the advertising campaign. One of the variables measured was whether the business was considering becoming a client of the bank. Of the businesses sampled, 50 of the 300 businesses reported that they were considering becoming a client of the bank. A hypothesis test was conducted to determine if this provides evidence that less than 20% of all businesses were considering becoming a client of the bank. Calculate the test statistic to two decimal places (2dp). Test statistic =

Researchers selected 848 patients at random among those who take a certain widely-used prescription drug daily. In a clinical trial, 18 out of the 848 patients complained of flulike symptoms. Suppose that it is known that 1.6% of patients taking competing drugs complain of flulike symptoms. Is there sufficient evidence to conclude that more than 1.6% of this drug's users experience flulike symptoms as a side effect at the a = 0.01 level of significance? ... 10, the sample size is Because npo (1-Po) = population size, and the patients in the sample requirements for testing the hypothesis (Round to one decimal place as needed.) satisfied. 5% of the selected at random, all of the

Researchers studying the link between prenatal vitamin use and autism surveyed the mothers of a random sample of children aged 24 - 60 months with autism and surveyed another separate random sample for children with typical development. Table summarizing the number of mothers in each group who did and did not use prenatal vitamins during the three months before pregnancy (data from Schmidt, 2011) Autism Typical Development Total No vitamin 111 70 181 Vitamin 143 159 302 Total 254 229 483 Complete the hypothesis test for independence between the two variables, use of prenatal vitamins during the three months before pregnancy and autism in Rguroo. What is the value of the test statistic for this test? (Use the Large Sample Z method and please round to two decimal places)

A study was conducted to examine the effects of yoga on feelings of anxiety and stress among 200 college students. 100 students were randomized to participate in daily yoga exercises in the morning, while the remaining 100 students were attended a wellness course that described the benefits of yoga and exercise on one's health. At the end of the study, it was determined that those who participated in daily yoga exercises had fewer symptoms of anxiety and stress compared to those who attended the wellness course. la. What is the study design that the investigators used? a. Case report b. Case series c. Ecological Study d. Cross-sectional (descriptive) e. Cross-sectional (analytic) f. Case-control study g. Retrospective cohort study h. Prospective cohort study i. Randomized clinical trial Ib-Would blinding have been feasible for this study? If yes, who could have been blinded? Circle all that apply. a. Subjects/Students b. Investigators c. Data analysts

A card company claims that 80% of all American college students send a card to their mother on Mother's Day. You take a random sample of 125 American college students and find that 70% of them sent a card to their mother on Mother's Day. At a .05 alpha level, can you prove or disprove the card company's claim? Show all work.