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- A school administrator wants to see if there is a difference in the number of students per class for the Portland Public School district (Group 1) compared to the Beaverton School district (Group 2). Let be the average number of students per class for the Portland Public School district. Let ₂ be the average number of students per class for the Beaverton School district. Assume the populations are normally distributed. A random sample of 25 Portland classes found a mean of 38 students per class with a standard deviation of 3. A random sample of 28 Beaverton classes found a mean of 35 students per class with a standard deviation of 4. a. Find a 95% confidence interval for the difference of the means. Use Excel Two Means Calculator found in the Course and round answers to 2 decimal places. <1-1₂< b. Select the correct conclusion based on the above confidence interval. Since the above confidence interval gives only negative values, we have 95% confident that the average number of students…A gardener was doing a study on the number of roses produced from a random sample of rose bushes. The following data represents the number of roses from his sample: 8 7 8 5 9 8. 6 7 7 10 14 Find the following statistical values to represent his data: a) The mean: (round to 1 decimal) b) The median: c) The mode: d) The sample standard deviation: (round to 1 decimal) e) The range:he accompanying data are x = advertising share and y = market share for a particular brand of cigarettes during 10 randomly selected years. x 0.103 0.073 0.071 0.077 0.086 0.047 0.060 0.050 0.070 0.052 y 0.132 0.126 0.122 0.086 0.079 0.076 0.065 0.059 0.051 0.039 (a) Calculate the equation of the estimated regression line. (Round your answers to six decimal places.)y = Obtain the predicted market share when the advertising share is 0.09. (Round your answer to five decimal places.)(b) Compute r2. (Round your answer to three decimal places.)(c) Calculate a point estimate of ?. (Round your answer to four decimal places.)On how many degrees of freedom is your estimate based?
- I. 6) Suppose that you score 79 on Exam 3. If the average score is 85, and the variance is 23.04, your z-score is: a) 0.26 b) -0.26 c) 1.25 d) -1.25 e) -2.05What is the difference between Micro and M? a. Micro (u) is the variance and M is the mean b. Micro (u) i sthe median and M is the mean c.Micro (u) is the mean of the sample and M is the mean of the population d. Micro (u) is the mean of the population and M is the mean of the sampleA simple random sample of 10 UE students were taken to estimate the mean (μ) weekly allowance of all UE students. The data are: 500 550 600 1000 675 450 500 650 800 825 1. Construct a 95% C.I. on μ and interpret. 2. Construct a 99% C.I. on μ and interpret.
- 2. Which of the following statements defines the 97.5th percentile value for a data sample, regardless of the sample data distribution? The value that is 97.5% larger than the sample mean. The value such that 2.5% of the sample observations are larger than this value, and 97.5% of the sample observations are smaller than this value. The value such that 97.5% of the sample observations are larger than this value, and 2.5% of the sample observations are smaller than this value. This value always corresponds to the sample mean plus 2 standard deviations.B. Samples of size n were randomly selected from populations with means and variance given below. In each case, find the mean and variance of the sampling distribution of the means. 1. n= 4 2. n= 4 3. n= 4 4. n= 5 5. n = 6 議 µ = 5.5 µ = 7.5 p = 8.5 p = 15 H = 20 2 = 25 2 = 9 0? = 16 {? = 30 0? = 36Suppose that the time in minutes it takes a student to complete an assignment is normally distributed with a mean 50 and variance 100 then the 85th percentile of the average time it takes a random sample of 25 students to complete the assignment is closest to a 48. • b. 52 • C. 40. • d. 60. • e. 71.
- Q5) The following data represent the yield on 90 consecutive batches of ceramic substrate to which a metal coating has been applied by a vapor-deposition process. Find the sample mean, median, variance and coefficient of variation of the given data. 94.186.1 95.3 84.9 88.8 84.6 94.4 84.1 93.2 90.4 94.1 78.3 86.4 83.6 96.1 83.7 90.6 89.1 97.8 89.6 85.1 85.4 98.0 82.9 91.4 87.3 93.1 90.3 84.0 89.7 85.4 87.3 88.2 84.1 86.4 93.1 93.7 87.6 86.6 86,4 86.1 90.1 87.6 94.6 87.7 85.1 91.7 84.5 95.1 95.2 94.1 96.3 90.0 86.1 92.1 94.7 89.4 90,6 89.6 90.0 90.1 92.4 94.3 96,4 87.3 93.2 88.2 86,6 86.7 86,4 91.1 88.6 92.4 84.1 94.3 90.6 82.6 97.3 91.2 83.0 85.0 89.1 83.1 96.8 87.5 84.2 85.1 90.5 95.6 88.3The government is interested to estimate the proportion of families gathering in the weekends, in a city. The city is divided into three blocks. A stratified random sample of 60 households was selected proportionately from each block considering the blocks as strata. The summary data of the survey are presented in the following table. Stratu Ni m (i) |X; Mean S; Pi 1 120 18 35.0 4.0 0.5 О.2 0.9 130 15 20.0 5.0 180 27 30.0 6.0 25 i) Estimate the proportion of family gathering in the weekend, and obtain a 95% confidence interval of your estimate. Interpret the results. ii) Find the appropriate sample size and its allocation for estimating the total family gathering, with a bound of 50 points on the error of estimation. Assume that the stratum standard deviations are o1=8, 02=12 and , o3=4. LO NO Oold 23Q2. Answer the following two questions under the assumption of normal populations with equal vari- ances. (a) The following are the numbers of sales which a random sample of nine salesmen of industrial chemicals in California and a random sample of six salesmen of industrial chemicals in Oregon made over a fixed period of time: (California) x; : 40, 46, 61, 38, 55, 63, 36, 60, 51 (Oregon) y; : 33, 62, 44, 54, 23, 42 Using s 5% level of significance, test whether or not California salesmen are more efficient in general. Write down the null and alternative hypothesis first. (b) Suppose that we wish to investigate whether males and females earn comparable wages in a cer- tain industry. Sample data show that 14 randomly surveyed males earn on the average $213.5 per week with a standard deviation of $16.5, while 18 randomly surveyed females earn on the average $194.1 per week with a standard deviation of $18.0. Let µi denote the average wage of males and 42 the average of females. Using a…