7. [Multiple Choices}(d)of rhesus monkeys that live in a captive breeding facility and were assigned to research studies is (0.67,0.83). Which of the following is true?Based on a random sample of 120 rhesus monkeys, a 95% confidence interval for the proportionCircle only ONE correct answer in each question. No explanations needed.(a)Which of the following is true regarding the Central Limit Theorem (CLT)?(i) 95 of the sampled monkeys were assigned to research studies(i) If your sample size is n = 30 exactly, then you are guaranteed to have an approximately normalsampling distribution of the sample mean.(ii) the margin of error for the confidence interval is 0.16(iii) a larger sample size would yield a wider confidence interval(ii) As the sample size n increases, the data distribution should become approximately normal.(iv) none of the above are true(iii) The Central Limit Theorem states that the sampling distribution of the sample mean should alwayshave the same shape as the population distribution.(e)evaluate the test results to determine if there is enough evidence toComplete the following sentence: When conducting a hypothesis test, weand then(iv) none of the above(i) Assume that the null hypothesis is false; accept the null hypothesis(b)sample of 10 teenage girls, would the sampling distribution of average BMI follow an approximately normalSuppose the population distribution of BMI among teenage girls is right-skewed. If you took a(ii) Assume that the null hypothesis is true; reject the null hypothesisdistribution?(iii) Assume that the alternative hypothesis is true; reject the null hypothesis(i) Yes, because the shape of the population distribution does not affect the shape of the sampling(iv) Assume the alternative hypothesis is false; reject the alternative hypothesisdistribution(ii) No, because the underlying population distribution is right-skewed, so no matter the sample size thesampling distribution cannot be normal.(iii) Yes, because we have more than ten observations, and according to the Central Limit Theorem thatis large enough for the sampling distribution to be close to bell-shaped even though the underlyingpopulation distribution is right-skewed(f)of the following would be plausible 95% confidence interval for u?Suppose a t-test yields a p-value of 0.02 when testing hypotheses Ho: µ = 0 vs Ha: µ > 0. Which(i) (1.3, 3.4)(ii) (-3.4, 1.3)(iї) (-1.3, 3.4)(iv) No, because the underlying population distribution is right-skewed and we have less than 30 obser-vations, which is the cutoff used for the Central Limit Theorem to apply.(iv) (-3.4, -1.3)(c)birth weight of rhesus monkeys born in captivity. Below are the summary statistics of the data and outputfrom the analysis testing if the true average birth weight of the monkeys is 0.4kg. What is the correctcalculation to estimate the true average birth weight of rhesus monkeys with a 95% confidence interval?Veterinarians at a nonhuman primate research center are interested in estimating the true average(g)linear regression to explore the relationship between the number of calories and amount of carbohydrates(in grams) Starbucks food menu items contain. The estimated regression equation with carbohydratesas the response variable and the calories as the explanatory variable is ŷstatistics of the two variables is provided below.Seventy-six Starbucks food items were analyzed for the calorie and carbohydrate content. We used= 8.94 + 0.11x, and summaryminQ1 medianQ3max meansdn missing0.27 0.370.39 0.5 0.68 0.44 0.12 10variable minQ1 median Q3sdn missingmaxmeancalories80 300350 420500338.8105.4 779, p-value = 0.306alternative hypothesis: true mean is not equal to 0.4t = 1.0853, df =carbohydrates163145 598044.916.6 7795 percent confidence interval:ХXXXXXX XXXXWhich of the following is a true statement regarding the slope?(i) There is a positive association between calorie and carbohydrate content; however, because the slope(=0.11) is small, the association between calories and carbohydrates is weak.(i) 0.44 + 1.0853 × 0.12/V9(ii) 0.44 ±1.0853 × 0.12(ii) A food item that has 100 calories above average is expected to have 11 more gram carbohydratesover the average carbohydrates in the data.(iii) 0.44± 2.26 × 0.12//10(iv) 0.39 ± 1.96 × 0.12(iii) Because a the lowest calorie content of food observed is 80, and the slope 0.11 is well below thislowest value, this is extrapolation and cannot be trusted.(iv) All statements are true.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose Diane and Jack are each attempting to use a simulation to describe the sampling distribution from a population that is skewed left with mean 50 and standard deviation 5. Diane obtains 1000 random samples of size n= 3 from the population, finds the mean of the means, and determines the standard deviation of the means. Jack does the same simulation, but obtains 1000 random samples of size n=40 from the population. Complete parts (a) through (c) below. (c) What do you expect the standard deviation of Diane's distribution to be? What do you expect the standard deviation of Jack's distribution to be? Diane's distribution is expected to have a standard deviation of Jack's distribution is xpected to have a standard deviation of (Round to two decimal places as needed.)
For a sample of 42 rabbits, the mean weight is 5 pounds and the standard deviation of weights is 3 pounds. Which of the following is most likely true about the weights for the rabbits in this sample? (A) The distribution of weights is approximately normal because the sample size is 42, and therefore the central limit theorem applies. (B) The distribution of weights is approximately normal because the standard deviation is less than the mean. (C) The distribution of weights is skewed to the right because the least possible weight is within 2 standard deviations of the mean. (D) The distribution of weights is skewed to the left because the least possible weight is within 2 standard deviations of the mean. (E) The distribution of weights has a median that is greater than the mean.
(a) There are many situations in which we want to compare means from populations having standard deviations that are equal. This method applies even if the standard deviations are known to be only approximately equal. Consider a report regarding average incidence of fox rabies in two regions. For region I, n, = 14, x, = 4.75, and s, = 2.84 and for region II, n2 = 13, x2 = 3.95, and sz = 2.41. The two sample standard deviations are sufficiently close that we can assume o, = 0,. Use the method of pooled standard deviation to consider the report, testing if there is a difference in population mean average incidence of rabies at the 5% level of significance. (Round your answer to three decimal places.) It =
1. Student's t test for correlated groups really reduces to _________. a. the sign test b. Student's t test for single samples using difference scores c. Students t test for independent groups d. none of the above 2. The z test for independent groups is seldom used because _________. it lacks sensitivity it is too complicated we seldom know the population variances the sampling distribution of z under H0 is unknown 3. In a t test, when the size of the sample is increased, the confidence interval _________. increases decreases stays the same changes shape a and d 4. As the df increases, the t distribution _________. gets more symmetrical approaches the normal distribution stays the same becomes more skewed
5. You form a distribution of the means of all samples of size 9 drawn from an infinite population that is skewed to the left. The population from which the samples are drawn has a mean of 50 and a standard deviation of 12. Which one of the following statements is true of this sampling distribution? (a) µz = 50, ơ, = 12 , the sampling distribution is skewed somewhat to the left. (b) u, = 50, ơ, = 4, the sampling distribution is skewed somewhat to the left. (c) u, = 50, o, =12 , the sampling distribution is approximately normal. (d) µ, = 50, o, = 4 , the sampling distribution is approximately normal.
Which of the following best describes the Central Limit Theorem? (A) All of these choices are correct (B) The sample mean is close to 0.50. (C) The underlying population is normal. (D) If the distribution of a random variable is non-normal, the sampling distribution of the sample mean will be approximately normal for samples n ≥ 30.
A pizza shop sells pizzas in four different sizes. The 1,000 most recent orders for a single pizza resulted in the following proportions for the various sizes. Size (inches) 12 Proportion 14 16 0.15 0.30 0.50 0.05 18 With x = the size of a pizza in a single-pizza order, the given table is an approximation to the population distribution of x. (a) Write a few sentences describing what you would expect to see for pizza sizes over a long sequence of single-pizza orders. % of the single-pizza orders for 12 inch pizza, In the long run, we would expect to see approximately % for 18 inch pizza. (b) What is the approximate value of P(x < 16)? (c) What is the approximate value of P(x ≤ 16)? % for 14 inch pizza, % for 16 inch pizza, and
1. If we take samples of size 10 from a population with p=.1 then the sampling distribution for the sample proportions is left skewed. true or false 2. The sampling distribution models, for samples coming from a given population, will become wider and wider as the sample size increases. true or false

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