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- In a large field the number of chafer beetles in an area A is thought to follow a Poisson distribution with a mean 2A. In order to measure the number of beetles in the field an entomologist plans to count all the beetles in a circle of radius r. How big does r have to be so that the chance there are no beetles in the circle is 0.01?For any sample of size 120 the population mean, the mean of the sampling distribution for the sample means, and the sample mean will always be equal to each other. True or False When using the central limit theroem for means with n = 68, it is not necessary to assume the distribution of the population data is normally distributed. True or False The symbole op represents the standardThe factor(s) to be considered when assessing if the Central Limit Theorem holds is/are the shape of the dis\\tribution of the original variable. the sample size. both of the above. none of the above; we only need n≥30n≥30.
- Suppose that 2 balls are randomly selected from an urn containing 3 red, 4 blue, and 5 white balls. If we let X and Y denote, respectively, the number of red and white balls chosen . Hint: This is an extension of Hypergeometric distribution. Round off your answer into number with 4 decimal places (for example 0.9452). Solve for P(X=2).A local restaurant claims that it gets 45 percent of its customers from Monday through Thursday, 20 percent on Friday, 20 percent on Saturday, and 15 percent on Sunday. How many degrees of freedom should be used to conduct a chi-square goodness-of-fit test of the claim?A concrete beam may fail either by shear (S) or flexure (F). Suppose that three failedbeams are randomly selected and the type of failure is determined for each one. Let X= the number of beams among the three selected that failed by shear. List eachoutcome in the sample space along with the associated value of X
- Mario made a claim that 95% of college male students in their school join triathlon. His friend, Baste, finds this hard to believe and decided to check the validity of such claim, so he took a random sample and found out that 75 out of 90 had joined the race. 1. What is the population proportion? 2. What is the sample proportion? 3. Is the sample large enough to use the Central Limit Theorem?Which of the following is NOT a condition that ALWAYS has to be satisfied to apply the Central Limit Theorem to the sample mean? a) The sample size must be larger than 30 b) There are no obvious outliers in the sample if the sample size is less than 30 c) There are no extreme outliers in the sample if the sample size is at least 30. d) The sample observations are independent.A college claims that the proportion, p, of students who commute more than fifteen miles to school is less than 15%. A researcher wants to test this. A random sample of 260 students at this college is selected, and it is found that 25 commute more than fifteen miles to school. Is there enough evidence to support the college’s claim at the 0.10 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. A. State the null hypothesis H0 and the alternative hypothesis H1 B. Would (Z) (t) (Chi-square) or (F) be the best statistic to use? C. Find the value of the test statistic. (Round to three or more decimal places.) D. Find the critical values. (Round to three or more decimal places.) E. Is there enough evidence to support the claim that the proportion of students who commute more than fifteen miles to school is less than 15%? (Yes or no)