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- A college professor suspects that students at his school are getting less than 8 hours of sleep a night, on average. To test his belief, the professor asks a random sample of 28 students, "How much sleep did you get last night?" Here are the data (in hours): 9 6 8 6 8 8 6 6.5 6 7 9 4 3 4 5 6 11 6 3 6 6 10 7 8 4.5 9 7 7 Do these data provide convincing evidence at the a = 0.05 significance level in support of the professor's suspicion?11. Add 6 to each number in the dataset. Then, the 15th percentile is:a. 1b. 6c. 8d. 7Use the following information to answer questions 12-14: Suppose the probability that an adult gets thenews from Facebook is 0.60. A random sample of 14 adults were surveyed to determine X, the numberof adults who get their news from Facebook.12. Which of the following statements is false?a. The set of possible x-values is {1, 2, 3, . . ., 14}b. X ~ B (14, 0.60)c. P(X=5) = 0.0408d. µ = 8.413. Find the probability that at least 6 adults get their news from Facebook.a. 0.8499b. 6/14c. 0.6429d. 0.941714. X is of data of type:a. categorical nominalb. categorical ordinalc. numerical continuousd. numerical discrete15. Suppose that the ages of Brunswick CC students are normally distributed. A random sample of 6Brunswick CC students reported the ages of 20, 35, 18, 45, 27, and 20 years old. Find the errorbound that corresponds to the 90% confidence interval for the true population mean age ofBrunswick CC…A psychologist found a study which claiming that 32% of patients who visit a psychologist have symptoms of anxiety. This psychologist had 44 patients visit. Let x = the number of patients that had symptoms of anxiety. (a) The random variable is which of the following? O the number of psychologists O the number of patients who visited the psychologist the number of patients who had symptoms of anxiety O the number of patients without symptoms of anxiety (b) How many total patients did the psychologist have visit?
- 4. Sampling distribution of the mean: The concentration of NOx (a set of criteria pollutants) in Los Angeles County has the following characteristics: µ = 700 ppm, σ = 30 ppm. [8 pts total] a. If you take 30 additional air samples, what is the probability that your sample mean will be greater than 710 ppm? Report 2 significant figures. % b. Discuss how increasing the sample size from 30 to 50 would affect the probability of the sample mean exceeding 710 ppm. What implications does this have for the accuracy of environmental monitoring? The probability would: Implications for environmental monitoring: O Increase O DecreaseProblem Solving. Solve the following problems. No immediate rounding. Round off final answers to three decimal places. A protective enchantment which alerts the Charms professor when a death eater attacks a magical school is designed to have a 90% reliability rate. Suppose that the nine magical schools equipped with this enchantment experienced an attack from the death eaters. Define the random variable X as the number of Charms professors alerted out of nine. Assuming that protective enchantment alerts are independent 1. Write down the associated PMF of X. 2. Compute for the probability of alerting at least 7 Charms professors.3. Can SAT scores predict college performance? Let x be a variable that represents SAT score of a computer science major, and let y be a variable that represents a student’s GPA upon graduation. A random sample of n =15 computer science majors provided their SAT scores and GPAs: x 1232 1070 1086 1287 1130 1048 1121 1095 1135 1208 1333 1160 1186 1243 1261 y 3.52 2.91 2.4 3.47 3.47 2.37 2.4 2.24 3.02 3.32 3.59 2.54 3.19 3.71 3.58 The scatter diagram for the SAT score and GPA is given below: (a) Find the sample correlation coefficient r. Truncate to two decimal places. What does the value tell you about the data? (b) Find the equation of the least squares line . Truncate to four decimal places. What does the slope mean? (c) Find the value of the coefficient of determination . Truncate to two decimal places. What does this number mean? (d) What is the predicted GPA if a computer science major got a…
- The probability is 0.4 that a traffic fatality involves an intoxicated or alcohol-impaired driver or nonoccupant. In six traffic fatalities, find the probability that the number, Y, which involve an intoxicated or alcohol-impaired driver or nonoccupant is a. exactly three; at least three; at most three. b. between two and four, inclusive. c. Find and interpret the mean of the random variable Y. a. The probability that exactly three traffic fatalities involve an intoxicated or alcohol-impaired driver or nonoccupant is nothing. (Round to four decimal places as needed.) The probability that at least three traffic fatalities involve an intoxicated or alcohol-impaired driver or nonoccupant is nothing. (Round to four decimal places as needed.) The probability that at most three traffic fatalities involve an intoxicated or alcohol-impaired driver or nonoccupant is nothing. (Round to four decimal places as needed.) b. The probability that between two and four…ASK YOUR TEACHER Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail.t An insurance company is studying wheat hail damage claims in a county in Colorado. A random sample of 16 claims in the county reported the percentage of their wheat lost to hail. 14 7 10 11 12 19 14 11 9 8 23 19 13 7 10 7 The sample mean is x = 12.1%. Let x be a random variable that represents the percentage of wheat crop in that county lost to hail. Assume that x has a normal distribution and a = 5.0%. Do these data indicate that the percentage of wheat crop lost to hail in that county is different (either way) from the national mean of 11%? Use a = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? O Ho: H = 11%; H,: µ 11%; right-tailed O Ho: H + 11%; H,: u = 11%; two-tailed O Ho: H = 11%; H,: u + 11%; two-tailed (b) What sampling distribution will you use? Explain the rationale for your…According to Reader's Digest, 44% of primary care doctors think their patients receive unnecessary medical care. Use the z-table. a. Suppose a sample of 260 primary care doctors was taken. Show the sampling distribution of the proportion of the doctors who think their patients receive unnecessary medical care. E(p)= (to 2 decimals) (to 4 decimals) b. What is the probability that the sample proportion will be within ±0.03 of the population proportion? Round your answer to four decimals. c. What is the probability that the sample proportion will be within ±0.05 of the population proportion? Round your answer to four decimals. d. What would be the effect of taking a larger sample on the probabilities in parts (b) and (c)? Why? The probabilities would - Select your answer -increasedecreaseItem 5 . This is because the increase in the sample size makes the standard error, ,
- A pathologist has been studying the frequency of bacterial colonies within the field of a microscope using samples of throat cultures from healthy adults. Long-term history indicates that there is an average of 2.80 bacteria colonies per field. Let r be a random variable that represents the number of bacteria colonies per field. Let O represent the number of observed bacteria colonies per field for throat cultures from healthy adults. A random sample of 100 healthy adults gave the following information. 2 3 4 5 or more 13 18 28 16 17 8 (a) The pathologist wants to use a Poisson distribution to represent the probability of r, the number of bacteria colonies per field. The Poisson distribution is given below. P(r) = r! Here 1 = 2.80 is the average number of bacteria colonies per field. Compute P(r) for r = 0, 1, 2, 3, 4, and 5 or more. (Round your answers to three decimal places.) P(0) = P(1) = Р(2) Р(3) 3 P(4) = %3D P(5 or more) = (b) Compute the expected number of colonies E = 100P(r)…How can I solved Question d and e?If two large random samples are drawn from two populations, each having a mean of $100, the relevant sampling distribution of their difference has a mean of a. 200 b. The Sum of the 2 Sample Means C. 0 D. The difference between the two sample means.
