A corporation is sampling without replacement forn = 3 firms to determine the one from which to purchase certain supplies. The sample is to be selected from a pool of six firms, of which four are local and two are not local. Let Y denote the number of non-local firms among the three selected. (a) P(Y = 1)

A population consists of the following 6 values: {10, 20, 30, 40, 50, 60}. A sample of size 3 will be chosen from this population without replacement and the median of the sample will be computed: { (0.5 (£n/2 + £n/2+1) m = x(n+1)/2 n odd n even In other words, in a sample of size n = 3 ordered from smallest to largest the median is the 2nd number. The median of a discrete random variable, μ, is defined as the value of such that and P(X M) ≤ 0.5 Determine the median of the population. Think of the population as an equally likely sample space. Determine the sampling distribution of the sample median, m for this population by (1) identifying all possible samples (how many are there?), (2) calculating the median in each sample and (3) using that to determine the probability of each median. Calculate E (m) Determine the standard error or the sample median

4 A political poll is assessing the relative strengths of two presidential candidates. A value of + 1 is assigned to every person who states a preference for candidate A and a value of -1 is assigned to anyone who indicates a preference for candidate B.a) Find the sample mean if 60% of those polled indicate a preference for candidate A.b) Write an expression for the sample mean as a function of the sample size and thepercentage of those polled that are in favor of candidate A.c) Find the sample size necessary to estimate the percentage of persons in favor ofcandidate A with a standard deviation no greater than 0. 1 %

Determine whether the samples are independent or dependent. A data set includes systolic blood pressure measurements from each of 230 randomly selected men and 230 randomly selected women. Choose the correct answer below. OA. The samples are independent because there is not a natural pairing between the two samples. OB. The samples are dependent because there is a natural pairing between the two samples. OC. The samples are independent because there is a natural pairing between the two samples. OD. The samples are dependent because there is not a natural pairing between the two samples.

Caffeine A student study of the effects of caffeine asked volunteers to take a memory test 2 hours after drink-ing soda. Some drank caffeine-free cola, some drank regular cola (with caffeine), and others drank a mixtureof the two (getting a half-dose of caffeine). Here are the5-number summaries for each group’s scores (number ofitems recalled correctly) on the memory test:a) Describe the W’s for these data.b) Name the variables and classify each as categorical orquantitative.c) Create parallel boxplots to display these results as bestyou can with this information.d) Write a few sentences comparing the performances ofthe three groups.

A recent poll indicates that 48% of all registered voters in America plan to vote for a specific candidate in the upcoming presidential election. Suppose a random sample of 20 Americans is taken. Let X represent the sample count who plan to vote for the candidate. What is P(X≠5)? 

A researcher is interested in understanding if there is a difference in the proportion of undergrad and grad students at UCI who prefer online teaching to in person teaching, at the a = 0.05 level. They take 2 samples, first, a sample of 300 undergrad students. The second, is a sample of 172 grad students. Of the undergrads, 186 said they preferred online lectures, and of the graduate students, 104 said that they prefer online lectures. Let p₁ = the proportion of undergrad students who prefer online class and p2 = the proportion of grad students who prefer online lectures. (a) Set up the null and alternative hypothesis (using mathematical notation/numbers AND interpret them in context of the problem). (b) Calculate the test statistic. (c) Calculate the critical value. (d) Draw a picture of the distribution of the test statistic under Ho. Label and provide values for the critical value and the test statistic, and shade the critical region. (e) Make and justify a statistical decision at…

In a study of pain relievers, 50 people were given product A, and 40 experienced relief. In the same study, 100 people were given product B, and 89 experienced relief. Fill in the blanks below to make the most reasonable statement possible. Product (Choose one) performed better in the study. That is because only% failed to get relief with this product, whereas failed to get relief with Product (Choose one) ▼ X S Esp i ! A M

1. For her botany class project, Jennifer wonders if there is a connection between the average weight of watermelons a vine produces and the root depth of the vine. Jennifer suspects that vines with deeper roots have a better water supply and produce larger melons. From a large watermelon field, 10 vines are chosen at random. At the end of 8 weeks, the watermelons are removed from each vine and the average weight of the watermelons from each vine is determined. Each plant is carefully dug up and its root depth (or length) is measure. Let x represent the root depth (to the nearest inch) and y be the mean weight of the watermelons on the vine (in pounds). Suppose that x = 17, s, = 6, y = 12, s, = 5.1, and r = = 0.93. a. Find the equation of the least squares regression line (round a and b to the nearest tenth). b. List 2 points that you know will be on the least-squares line you found in part a. c. What percent of variation is accounted for by a linear relationship? d. Using part a.,…

The table below shows the number of male and female students enrolled in nursing at a university for a certain semester. A student is selected at random. Complete parts (a) through k (d). Males Females Total Nursing majors 93 700 793 Non-nursing majors 1015 1723 2738 Part 3 of 4 Total 1108 2423 3531 P(not being female or being a nursing major) = (Round to the nearest thousandth as needed.). (a) Find the probability that the student is male or a nursing major. P(being male or being nursing major) = 0.512 (Round to the nearest thousandth as needed.) (b) Find the probability that the student is female or not a nursing major. D P(being female or not being a nursing major) = 0.974 (Round to the nearest thousandth as needed.) (c) Find the probability that the student is not female or a nursing major. H C n 101 √₁ Vi L (0,0) 4 x