Consider the population described by the probability distribution shown below. The random variable is observed twice with independent observations. X P(x) 3,3 3,4 3,5 3,6 4,3 4,4 4,5 4,6 Full data set 0.06 0.09 0.09 0.06 0.06 0.06 3 0.3 4 0.3 5 0.2 6 0.2 Sample Probability 0.09 0.09 Sample 5,3 5,4 5,5 5,6 6,3 6,4 6,5 6,6 Probability 0.06 0.06 0.04 0.04 0.06 0.06 0.04 0.04 a. Complete the sampling distribution table. Type the x values in ascending order. 3.5 4 X Probability 0.09 (Type exact answers in simplified form.) 0.24 0.16 5.5 6
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- Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. A researcher was interested in comparing the GPAs of students at two different colleges. Independent simple random samples of 8 students from college A and 13 students from college B yielded the following GPAs. College A 3.7 3.2 3.0 2.5 2.7 3.6 2.8 3.4 College B 3.8 3.2 3.0 3.9 3.8 2.5 3.9 2.8 4.0 3.6 2.6 4.0 3.6 Construct a 95% confidence interval for μ1−μ2, the difference between the mean GPA of college A students and the mean GPA of college B students. Round to two decimal places. (Note: x1=3.1125, x2=3.4385, s1=0.4357 s2=0.5485Choose an American household at random and let the random variable ?X be the number of cars (including SUVs and light trucks) they own. Given is the probability distribution if we ignore the few households that own more than 5 cars. Number of cars 0 1 2 3 4 5 Probability 0.09 0.36 0.35 0.13 0.05 0.02 About what percentage of households have a number of cars within 2 standard deviations of the mean?Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with ? = 2.5%. A random sample of 10 bank stocks gave the following yields (in percents). 5.7 4.8 6.0 4.9 4.0 3.4 6.5 7.1 5.3 6.1 The sample mean is = 5.38%. Suppose that for the entire stock market, the mean dividend yield is ? = 4.9%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.9%? Use ? = 0.01. (c) Find (or estimate) the P-value. (Enter a number. Round your answer to four decimal places.) ?Sketch the sampling distribution and show the area corresponding to the P-value. (Select the correct graph.)
- A variable y of a finite population has the frequency distribution shown in the table. Suppose a member is selected at random from the population and let Y denote the value of the variable y for the member obtained. Complete parts (a) through (d) below. y 4 5 6 7 1 1 13 5 a. Determine the probability distribution of the random variable Y. 4 6. 7 y P(Y = y) (Type integers or decimals. Do not round.) b. Use random-variable notation to describe the events that Y takes on the value 6, a value less than 6, and a value of at least 6. The event that Y takes on the value 6 can be represented as The event that Y takes on a value less than 6 can be represented as The event that Y takes on a value of at least 6 can be represented as c. Find P(Y = 6), P(Y 6). P(Y = 6) = (Type an integer or a decimal. Do not round.) P(Y<6) = (Type an integer or a decimal. Do not round.) P(Y 2 6) = (Type an integer or a decimal. Do not round.)Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail.† An insurance company is studying wheat hail damage claims in a county in Colorado. A random sample of 16 claims in the county reported the percentage of their wheat lost to hail. 16 6 8 9 10 18 14 13 9 10 25 18 13 8 14 3 The sample mean is x = 12.1%. Let x be a random variable that represents the percentage of wheat crop in that county lost to hail. Assume that x has a normal distribution and σ = 5.0%. Do these data indicate that the percentage of wheat crop lost to hail in that county is different (either way) from the national mean of 11%? Use ? = 0.01. (a) What is the level of significance? Compute the z value of the sample test statistic. (Round your answer to two decimal places.)(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)Consider the population described by the probability distribution shown below. The random variable is observed twice with independent observations. Sample Probability 0.16 0.12 0.04 0.08 0.12 0.09 0.03 0.06 p(x) 0,0 0,2 0,4 0,6 2,0 2,2 2,4 2,6 Full data set 0.4 0.3 4 4,0 4,2 4,4 4,6 Probability 0.04 0.03 0.01 0.02 0.08 0.06 0.02 0.04 0.1 Sample 6,0 6,2 6,4 6,6 0.2 a. Complete the sampling distribution table. Type the x values in ascending order. 1 2 6. Probability 0.16 0.22 0.13 (Type exact answers in simplified form.)
- Consider the population described by the probability distribution shown below. The random variable is observed twice with independent observations, as shown below. Complete parts a and b. Full data set X 3 4 5 6 p(x) 0.2 0.2 0.3 0.3 a. Complete the sampling distribution table. Type the medians in ascending order. Median 3 5 6 Probability || 0.08 0.24 (Simplify your answers. Type integers or decimals.) 4 0.18 (…) 0.04 Sample |3,3 3,4 3,5 Probability 0.04 0.06 Sample 5,3 5.4 Probability 0.06 0.06 3,6 4,3 0.06 0.04 4,4 4,5 4,6 0.04 0.06 0.06 5,5 5.6 6,3 6,4 0.09 0.09 0.06 0.06 6,5 6,6 0.09 0.09A variable y of a finite population has the frequency distribution shown in the table. Suppose a member is selected at random from the population and let Y denote the value of the variable y for the member obtained. Complete parts (a) through (d) below. y 3 4 6. f 1 1 11 7 a. Determine the probability distribution of the random variable Y. 3 y P(Y = y) (Type integers or decimals. Do not round.) b. Use random-variable notation to describe the events that Y takes on the value 5, a value less than 5, and a value of at least 5. The event that Y takes on the value 5 can be represented as The event that Y takes on a value less than 5 can be represented as The event that Y takes on a value of at least 5 can be represented as { }. c. Find P(Y = 5), P(Y 5). %3D P(Y = 5) = (Type an integer or a decimal. Do not round.) P(Y<5) = (Type an integer or a decimal. Do not round.) P(Y 2 5) = (Type an integer or a decimal. Do not round.) LONationally, about 11% of the total U.S. wheat crop is destroyed each year by hail.† An insurance company is studying wheat hail damage claims in a county in Colorado. A random sample of 16 claims in the county reported the percentage of their wheat lost to hail. 15 7 7 13 13 20 13 12 5 10 26 22 13 7 11 3 The sample mean is x = 12.3%. Let x be a random variable that represents the percentage of wheat crop in that county lost to hail. Assume that x has a normal distribution and σ = 5.0%. Do these data indicate that the percentage of wheat crop lost to hail in that county is different (either way) from the national mean of 11%? Use α = 0.01. (a) What is the level of significance? Compute the z value of the sample test statistic. (Round your answer to two decimal places.)(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)
- Suppose that x represents the number of cars sold at a dealership in a randomly selected single day. The probability distribution of x is given in the table below. 4 5 7 8 9 10 p(x) 0.03 0.08 0.19 0.31 0.22 0.13 0.04 If you wish, you can click to download the data in your preferred format. CrunchIt! CSV Excel JMP Mac Text Minitab PC Text R SPSS TI Calc What is the mean number of cars, u, sold per day at the dealership? Give your answer decimal form precise to two decimal places. carsce home Calendar Badges All courses Course dashboard The following table represents the probability distribution of the random variable X. Find P(X-3) 00 1 2 4 1/16 P(X) 2/16 3/16 10/16 Select one: O 1/16 O15/16 O10/16 5/16 estion 4 Identify which sampling method is used:Consider the population described by the probability distribution shown below. The random variable is observed twice with independent observations. Sample X p(x) 0.2 4 5 0.2 6 7 0.2 20000 NANNI. 0.4 4,4 4,5 4,6 4,7 5,4 5,5 5,6 5,7 Full data set Probability 0.04 0.04 0.08 0.04 0.04 0.04 0.08 0.04 Sample 6,4 6,5 6,6 6,7 7,4 7,5 7,6 7,7 Probability 0.08 0.08 0.16 0.08 0.04 0.04 0.08 0.04 a. Complete the sampling distribution table. Type the x values in ascending order. x 4.5 5 6.5 7 Probability 0.04 (Type exact answers in simplified form.) 0.24 0.24