While on an unauthorised trip to the local fast food restaurant during their study period, a pair of Year 12 students are convinced that they have just seen the Prime Minister buying a hamburger. On returning to the school, dp =1 p(1- p), where p is the their amazing discovery spreads throughout the school community at the rate proportion of the school community that has already heard the rumour, t minutes after their return to school. (a) What proportion of the school community has heard the rumour when it is spreading most rapidly? By the beginning of the afternoon period, 20% of the school community had already heard the rumour. (b) Find p(t), at time t minutes since the beginning of the afternoon period, given 10 1 1 1 %3D p(1-p) p p-1' (c) At what time (correct to the nearest minute) is the rumour spreading most rapidly?

GSS 2018 respondents were asked to rate their level of agreement to the statement, “Differences in income in America are too large.” Responses were measured on a 5-point scale: 1 = strongly agree, 2 = agree, 3 = neutral, 4 = disagree, and 5 = strongly disagree. Strong Democrats had an average score of 1.69 (s = 1.04, N = 86) while strong Republicans had an average score of 2.11 (s = 1.05, N = 67). The estimated standard error of the difference between meansis 0.17. What is the appropriate test statistic? Why? Test the null hypothesis with a one-tailed test (strong Democrats are more likely to agree with the statement than strong Republicans); α = .05. What do you conclude about the difference in attitudes for these two political groups? If you conducted a two-tailed test with α = .05, would your decision have been different?

A survey was conducted two years ago asking college students their top motivations for using a credit card. You think this distribution has changed. You randomly select 425 college students and ask each one what the top motivation is for using a credit card. Can you conclude that there has been a change in the distribution? Use a = 0.025. Complete parts (a) through (d). Response Old Survey % 29% New Survey Frequency, f Rewards 110 Low rates Cash back Discounts 23% 96 21% 109 7% 46 Other 20% 64 O B. The distribution of motivations is 110 rewards, 96 low rate, 109 cash back, 46 discounts, and 64 other. O C. The distribution of motivations is 29% rewards, 23% low rate, 21% cash back, 7% discounts, and 20% other. Which hypothesis is the claim? o Ho (b) Determine the critical value, Yo, and the rejection region. X = 11.143 (Round to three decimal places as needed.) Choose the correct rejection region below. Oc. X

It is bleieved that the percent of convicted felons who have a history of juvenile deliquency is 70%.  Is there evidence to support the claim that the actual percentage is more than 70% if out of 200 convicted felons, we find that 154 have a history of juvenile deliquency?  Set the level of significance at a = 0.05

Consider a medical test with a false positive rate of 1% and a false negative rate of 2%. The frequency of the condition in people who take this test is 3% Q4. If this test was given to 100,000 healthy people, how many false diagnoses would there be? Q5. What is the overall percentage of people who test "positive" who are actually negative for the condition? Q6. What is the overall percentage of people who test "negative" who are actually positive for the condition? # wrong diag. = ??? % pos. = ??? % % pos. = ??? %

Cory is serving coffee in a large reception with many guests. There are two kinds of coffee: regular anddecaf. So far, he has served 71 cups of regular and 49 cups of decaf.Question 3.Based on the information so far:(a) Estimate the proportion of coffee-drinking guests who prefer regular.

The first pic is the question, since I’ve been receiving some incorrect answers from the tutors, I included an example problem in the second pic.