A civil engineer has been studying the frequency of vehicle accidents on a certain stretch of interstate highway. Longterm history indicates that there has been an average of 1.76 accidents per day on this section of the interstate. Let r be a random variable that represents number of accidents per day. Let O represent the number of observed accidents per day based on local highway patrol reports. A random sample of 90 days gave the following information. 1 4 or more 2 18 12 24 20 16 (a) The civil engineer wants to use a Poisson distribution to represent the probability of r, the number of accidents per day. The Poisson distribution is given below. P(r) r! Here 1 = 1.76 is the average number of accidents per day. Compute P(r) for r = 0, 1, 2, 3, and 4 or more. (Round your answers to three decimal places.) P(0) P(1) - P(2) = Р(3) P(4 or more) (b) Compute the expected number of accidents E = 90P(r) for r = 0, 1, 2, 3, and 4 or more. (Round your answers to two decimal places.) E(0) = E(1) = E(2) Е(3) = E(4 or more) (c) Compute the sample statistic x? = E((0 - E)?/E) and the degrees of freedom. (Round your sample statistic to three decimal places.) df = (d) Test the statement that the Poisson distribution fits the sample data. Use a 1% level of significance. O Fail to reject the null hypothesis, there is sufficient evidence to conclude the Poisson distribution does not fit. Reject the null hypothesis, there is insufficient evidence to conclude the Poisson distribution does not fit. Reject the null hypothesis, there is sufficient evidence to conclude the Poisson distribution does not fit. O Fail to reject the null hypothesis, there is insufficient evidence to conclude the Poisson distribution does not fit.

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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 13 22 13 13 7 12 23 19 11 9 13 4 The sample mean is x = 12.4%. 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?  State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?  H0: μ ≠ 11%; H1: μ = 11%; two-tailedH0: μ = 11%; H1: μ ≠ 11%; two-tailed    H0: μ = 11%; H1: μ < 11%; left-tailedH0: μ = 11%; H1: μ > 11%; right-tailed (b) What sampling distribution will you…

Three randomly selected children are surveyed. The ages of the children are 1, 4, and 10. Assume that samples of size n = 2 are randomly selected with replacement from the population of 1, 4, and 10. Listed below are the nine different samples. Complete parts (a) through (d). 1,1 1,4 1,10 4,1 4,4 4,10 10,1 10,4 10,10 a. Find the value of the population variance o². 14 (Round to three decimal places as needed.) b. Find the variance of each of the nine samples, then summarize the sampling distribution of the variances in the format of a table representing the probability distribution of the distinct variance values. ▼ E 2 ▼ F (Type integers or simplified fractions.) Probability ▼ C

Three randomly selected children are surveyed. The ages of the children are 2​, 4​, and 12. Assume that samples of size n=2 are randomly selected with replacement from the population of 2​, 4​, and 12. Listed below are the nine different samples. Complete parts​ (a) through​ (d).     2​,2    2​,4    2​,12    4​,2    4​,4    4​,12    12​,2    12​,4    12​,12          a. Find the value of the population median.   enter your response here ​(Type an integer or a decimal. Do not​ round.) b. Find the median of each of the nine​ samples, then summarize the sampling distribution of the medians in the format of a table representing the probability distribution of the distinct median values.   Sample Median Probability ▼   4.8 2 6.4 enter your response here ▼   5 3 5.5 enter your response here ▼   1.2 2.8 4 enter your response here ▼   10 14 7 enter your response here ▼   16 13 8 enter your response here ▼…

a population proportion of 0.61. Suppose a random sample of 662 items is sampled randomly from this population

Three randomly selected children are surveyed. The ages of the children are 2, 3, and 10. Assume that samples of size n = 2 are randomly selected with replacement from the population of 2, 3, and 10. Listed below are the nine different samples. Complete parts (a) through (d). 2,2 2,3 2,10 3,2 3,3 3,10 10,2 10,3 10,10 a. Find the value of the population variance o². (Round to three decimal places as needed.)

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.)

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ASK YOUR TEACHER Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail.t 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. 14 7 10 11 12 19 14 11 9 8 23 19 13 7 10 7 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 a = 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 a = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? O Ho: H = 11%; H,: µ 11%; right-tailed O Ho: H + 11%; H,: u = 11%; two-tailed O Ho: H = 11%; H,: u + 11%; two-tailed (b) What sampling distribution will you use? Explain the rationale for your…