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- A survey shows that 64% of American teenagers want to be eventually be self-employed. A simple random sample of 540 teenagers is obtained. FindP(p?<.61) Would it be unusual to find that 400 or more teenagers in our sample wanted to eventually be self- employed?Z. Anursing school claims that more than 28% of its students plan to go into general practice. It is found that among a random sample of 130 of the school's students, 30% of them plan to go into general practice. Find the P-value for a test of the school's claim 0.3058 0.3037 O 0.4078 O 0.5076A travel agency wants to promote pleasure trips into space and wants to know which of the two commercial companies should they promote Virgin Galactic or Blue Origin? The one preferred by the customers will be the one they decide to promote. For this reason they take a random sample of 16 potential travelers, and they ask if they would prefer Virgin Galactic or Blue Origin. Let X be the number of travelers who preferred Virgin Galactic and let p=X/16 denote the corresponding proportion. Suppose that we want to show that Virgin Galactic is preferred to Blue Origin. Please formulate the null and alternative hypotheses and calculate the rejection region. Use α=0.05 Suppose that 11 out of 16 prefer Virgin Galactic and that α = 0.05, is this enough evidence to show that Virgin Galactic is preferred to Blue Origin? Perform the test and give your conclusion. Which company should they promote?
- According to the Rule of Three, when we have a sample size n with x=0 successes, we have 95% confidence that the true population proportion has an upper bound of 3/n. If 40 couples use a method of gender selection and each couple has a baby girl, what is the 95% upper bound for p, the proportion of all babies who are boys?Imagine you are doing a Related-Samples t-test, and you are on Step Two of the hypothesis test. The sample of difference scores that you calculated is -1, -1, -3, +2, 0, -4. If you are doing the test with α = .01, and two tails, what would he correct t-critical be?In studies for a medication, 7 percent of patients gained weight as a side effect. Suppose 565 patients are randomly selected. Use the normal approximation to the binomial to approximate the probability that (a) exactly 40 patients will gain weight as a side effect. (b) no more than 40 patients will gain weight as a side effect. (c) at least 51 patients will gain weight as a side effect. What does this result suggest? (a) P(40) = (Round to four decimal places as needed) (b) P(X< 40) = (Round to four decimal places as needed) (c) P(X251) = (Round to four decimal places as needed) Since 51 is than 7% of the patients, this suggests that the proportion of patients that gain weight as a side effect is 0.07.
- Imagine that you are collaborating with another researcher on a project. In your experiment, an initial sample of 40 participants randomly assigned to one of two groups (n=20 each) leads to an independent samples t-test result that doesn't quite reach statistical significance (p .08, which is so sad). Your collaborator proposes that you continue the experiment, adding 40 more participants (20 to each condition). Then, your collaborator reasons that, if p is lower than .05, you can publish your final sample size of n=80 with statistically significant results. convince your collaborator that there are problems with their proposalImagine you are doing a Related-Samples t-test, and you are on Step One of the hypothesis test. If you are doing the test with α = .05, and two tails, how would the H0 (null hypothesis) look?A sample of n=36 scores is selected from a normal population with μ=78 and σ=18. (a) What is the probability that the sample mean will be greater than 75? (b) What is the probablity that the sample mean will be less than 71?
- Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 250 numerical entries from the file and r = 60 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using α = 0.01. What does the area of the sampling distribution corresponding to your P-value look like? a. The area in the right tail of the standard normal curve. b. The area not including the right tail of the standard normal curve.…2. Use the normal approximation to the binomial with n=10 and p=0.5 to find the probability P(X27)Consider a binomial experiment with n=7 trials where the probability of success on a single trial is p=030. Find P(r=0) and Find P(r>1) using the complement rule.