A random variable L is being modelled as a discrete mixture of three Uniform distributions: Uniform on [0,10], Uniform on [0,20] and Uniform on [0,100]. You are given: 500 The median of L is 31 The mean of L is 33.5 Calculate the variance of L.
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- Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The mean shopping time, u, spent by customers at the supermarkets has been reported to be 35 minutes, but executives hire a statistical consultant and ask her to determine whether it can be concluded that u is greater than 35 minutes. To perform her statistical test, the consultant collects a random sample of shopping times at the supermarkets. She computes the mean of these times to be 42 minutes and the standard deviation of the times to be 10 minutes. Based on this information, answer the questions below. What are the null hypothesis (H,) and the alternative hypothesis (H,) that should be used for the test? H: u is ? H: u is ? In the context of this test, what is a Type I error? A Type I error is ? fact, u is ? ? v when, in v the hypothesis that u is? v? v. Suppose that the consultant decides to reject the null hypothesis. What sort of error might she be…Image has all the dataAssume the sample variances to be continuous measurements. Find the probability that a random sample of 31 observations, from a normal population with variance of 6, will have a sample variance between 3.33 and 9,99 Select one: Oa. 0.975 Ob. 0.011 Oc 0.985 Od. 0.965
- Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The mean shopping time, µ, spent by customers at the supermarkets has been reported to be 40 minutes, but executives hire a statistical consultant and ask her to determine whether it can be concluded that u is greater than 40 minutes. To perform her statistical test, the consultant collects a random sample of shopping times at the supermarkets. She computes the mean of these times to be 44 minutes and the standard deviation of the times to be 15 minutes. Based on this information, answer the questions below. What are the null hypothesis (H,) and the alternative hypothesis (H,) that should be used for the test? Hiµ is ? H: p is ? In the context of this test, what is a Type II error? A Type II error is ? fact, u is ? the hypothesis that u is when, in Suppose that the consultant decides not to reject the null hypothesis. What sort of error might she be making?Assume that we have estimated the standard deviation of a sample x₁,. ., xn ER using the sample standard deviation s = ô(x₁,x2,...,xn). What does ô(−2x1, −2x2,..., -2xn) equal? A: s B: -4s C: 4s D: -2s E: 2sAssume 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. %3D
- 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…s t n 16. The following are some of the particulars of the distribution of weight of boys and girls in a class : Girls Boys 100 50 Number Mean weight 60 kg 45 kg 4 Variance (a) Find the standard deviation of the combined data (b) Which of the two distributions is more variable ? (b), tn, o AL.For a distribution, the mean is 10, variance is 16, y, is + 1 and B, is 4. Obtain the first four moments about the origin, i.e., zero. Comment upon the nature of distribution.