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- The times to pop a regular bag of microwave popcorn without burning it are Normally distributed with a mean time of 140 seconds and a standard deviation of 20 seconds. The times to pop a mini bag of microwave popcorn, without burning it, are Normally distributed with a mean time of 90 seconds and a standard deviation of 15 seconds. Suppose two independent random samples, 25 of each, are taken and the mean popping times are calculated. Let R = the popping time of a randomly selected regular-sized bag and M = the popping time of a mini-sized bag. Which of the following best describes the mean of the sampling distribution of ? A) –50 B) 50 C) 90 D) 140In a trivariate distribution the simple coefficient of correlation are as follows if r12 = 0.76, rı3= 0.75 and r²3= 0.71 calculate the coefficient of partial correlation r 12.3The Wilcoxon signed-rank test can be used to perform a hypothesis test for a population median, η, as well as for a population mean, µ. Why is that so?
- Let X1, X2,..., Xn be a random sample of size n > 3 from a normal distribution with unknown mean μ and known variance equal to 2. Show that is an unbiased estimator of μ and compute its variance. pAssume that a high school principal believes that high number of absences hinders the students' ability to perform on standardized tests. He randomly selects a sample of 9 students who had 5 or more absences in the school year. The average ACT Composite score for this sample is X = 19 with s = 4.9. ACT Composite scores are normally distributed with u = 21.0. Do the data support the claim that the high number of absences hinders the students' ability to perform on standardized tests, using a = .05? Please show the four-step hypothesis test. %3DThe average height X and weight Y of males in population have a bivariate normal distribution with means µX 1.80 m., µy 90.0 kgs and standard deviations Ox = 0.30 m., oy = 15.3 kgs respectively. The correlation coefficient between X and Y is p= 0.80.
- The amount of gasoline in gallons sold by three different gas stations during one day is given by the independent random variables X1,X2, X3 each with a normal distribution. X1 has a mean µl =700 and standard deviation ơ1 55; X2 has mean u2 =700 and standard deviation o2 = 65; X3 has mean u3=900 and standard deviation 03 = 100. Suppose the prices per gallon are $2.90, $3.00 and $3.10 for X1, X2, and X3 respectively. Find the probability that the combined revenue for a given day is less than $6000. Use the z-score table. Round answer to the nearest hundredth.The table below shows the number of hours per day 11 patients suffered from headaches before and after 7 weeks of soft tissue therapy. At x = 0.01, is there enough evidence to conclude that soft tissue therapy helps to reduce the length of time patients suffer from headaches? Assume the samples are random and dependent, and the population is normally distributed. Complete parts (a) through (f). Patient 8 9 10 11 Q 1 Daily headache hours (before) 2.3 3.4 3.3 2.6 1.8 Daily headache hours (after) 1.8 2.7 1.8 1.6 1.9 1.9 1.2 2.5 2.2 2.0 1.1 2 3 4 5 6 7 4.1 3.2 3.5 2.4 3.7 2.6 C (a) Identify the claim and state Ho and Ha The claim is "The therapy the length of time patients suffer from headaches." Let μd be the hypothesized mean of the patients' daily headache hours before therapy minus their daily headache hours after it. State Ho and H₂. Choose the correct answer below. OA. Ho: Hd=d O C. Ho: Hd ≤0 OB. Ho. Họ sở Ha: Hd >d Ha: Hdd Ha: Hd>0 OD. Ho: Hd #d Ha:Hd=d O E. Ho: Hd zd Ha: Hd 3.169…Suppose that Y has an exponential distribution with mean Beta. Show that 2Y/Beta has a chi square distribution with 2 degrees of freedom.
- Let Y be the life in hours of a battery. Assume Y is normally distributed with mean 200 and variance o?. If a purchaser of such batteries requires that at least 90% of the batteries have lives exceeding 150 hours, what is the largest value o can be and still have the purchaser satisfied?Compute the value of the test statistic and ConclusionLet ex be a random variable that represents the hemoglobin count (HC) in human blood (measured in grams per milliliter). In healthy adult females, x has a approximately normal distribution with a population mean of 14.0 and population standard deviation equal 2.3. Suppose a female patient had 10 blood test over the past year , and the sample mean HC was determined to be 15.3. With a level of significance a= 0.05, determine whether the patient's HC is higher than the population averages. Specifically do the following: write the data state null hypothesis H0 and the alternate hypothesis H1
