Anystate Auto Insurance Company took a random sample of 368 insurance claims paid out during a leyear period. The average claim paid was $1580. Assume a = $240. Find a 0.90 confidence interval or the mean claim payment. (Round your answers to two decimal places.) lower limit $ upper limit $ Find a 0.99 confidence interval or the mean claim payment. (Round your answers to two decimal places.) lower limit $ upper limit $ The Wind Mountain archaeological site is located in southwestern New Mexico. Wind Mountain was home to an ancient culture of prehistoric Native Americans called Anasazi. A random sample of excavations at Wind Mountain gave the following depths (in centimeters) from present-day surface grade to the location of significant archaeological artifactst. 85 45 120 80 75 55 65 60 95 90 70 75 65 68 In USE SALT (a) Use a calculator with mean and sample standard deviation keys to find the sample mean x and sample standard deviation s. (Round your answers to four decimal places.) cm S cm (b) Compute a 90% confidence interval for the mean depth u at which archaeological artifacts from the Wind Mountain excavation site can be found. (Round your answers to one decimal place.) lower limit cm upper limit cmWhat are the requirements for a probability distribution? (Select all that apply.) C] The summation of the probabilities equal 1. C] Associated probabilities for each value of x. [:1 The summation of the probabilities is 1. C] Each probability takes on values between 0 and 1 inclusive. C] Each probability takes on a value of 0 or 1. C] Each value ofx has the same probability. C] A description of all the values of the random variable X. X The Orchard Cafe has found that about 20% of the diners who make reservations don't show up. If 70 reservations have been made, how many diners can be expected to show up? Find the standard deviation of this distribution. (Round your answers to two decimai places.) .11: X a: 3.35 y Briefly answer the following questions. (a) What is a null hypothesis H0? O A specific hypothesis where the claim is that the population parameter is equal to 0. O A working hypothesis making a claim about the population parameter in question. O A specific hypothesis where the claim is that the population parameter does not equal 0. Any hypothesis that differs from the original claim being made. X (b) What is an alternate hypothesis H1? O A specific hypothesis where the claim Is that the population parameter does not equal 0. O A specific hypotheSis where the claim is that the population parameter is equal to O. O Any hypothesis that differs from the original claim being made. C) A working hypothesis making a claim about the population parameter in question. (c) What is a type I error? 0 Type I error is rejecting the null hypothesis when it is false. 0 Type I error is failing to reject the null hypothesis when it is false. C) Type I error is rejecting the null hypothesis when it is true. O Type I error is failing to reject the null hypothesis when it is true. v/ What is a type 11 error? 0 Type 11 error is rejecting the null hypothesis when it is false. 0 Type 11 error is failing to reject the null hypothesis when it is false. '9 Type 11 error is rejecting the null hypothesis when it is true. 0 Type I] error is failing to reject the null hypothesis when it is true. X Let x be a random variable representing diVidend yield of bank stocks. We may assume that X has a normal distribution with a = 2.8%. 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 x : 5.38%. Suppose that for the entire stock market, the mean dividend yield is p : 4.0%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.0%? Use a = 0.01. (a) What Is the level of significance? :l State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? 0 H0: ,1 : 4%; H1: [1 > 4%; right-tailed O HO: ,1 z 4%; H1: ,1 4%; H1: [4 z 4%; right-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The Student's t, since we assume that x has a normal distribution with known a. O The Student's it, since n is large with unknown 0. O The standard normal, since we assume that X has a normal distribution with unknown 6. O The standard normal, since we assume that X has a normal distribution with known 0. Compute the 2 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.) Sketch the sampling distribution and show the area corresponding to the Pavalue. _ 03 2 1 0 1 Z 3 03 2 1 0 1 2 3 03 2 1 0 1 2 3 03 2 1 0 1 2 3 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a? O At the a = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. D At the a = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (e) State your conclusion in the context of the application. 0 There is sufficient evidence at the 0.01 level to conclude that the average yield for bank stocks is higher than that of the entire stock market. Q There is insufficient evidence at the 0.01 level to conclude that the average yield for bank stocks is higher than that of the entire stock market