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3. [0.46/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 10.3.004. Let x - age in years of a rural Quebec woman at the time of her first marriage. In the year 1941, the population variance of x was app one a recent study of age at first marr erval for the population variance (a] What is the level of significance? State the null and OH,: al > 5.1 # H,: al - 5.1; H,: 3 0.100 D D.050 a, we fail to ro the null hypothesis. Since the Puvalue > a, we reject the null hypothesis. # Since the P-value s a, we reject the null hypothesis. Since the Puvalue s a, we fall to reject the null hypothesis. c] Interpret your co islan in the context of the appl At the 5% level of significance, t ge at first marriage is less than 5.1. At the 5% level of significance, ther ence to cr e of age at first marriage is less than 5.1. (f ) Find the re ted confidence interval for the population variance. (Round your answers to two decimal places.) lower limit upper limitLet x represent the average annual salary of college and university professors (in thousands of dollars) in the United States. For all colleges and universities in the United States, the population variance of x is approximately ? = 47.1. However, a random sample of 15 colleges and universities in Kansas showed that x has a sample variance s? = 81.9. Use a 5% level of significance to test the claim that the variance for colleges and universities in Kansas is greater than 47.1. Find a 95% confidence interval for the population variance. a) What is the level of significance? State the null and alternate hypotheses. OH : ' > 47.1 OH,: 02 = 47.1; H,: 0 # 47.1 b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.) What are the degrees of freedom? What assumptions are you making about the original distribution? We assume a uniform population distribution. We assume a binomial population distribution. We assume a normal population distribution. We assume a exponential population distribution. (c) Find or estimate the P-value of the sample test statistic. P-value > 0.100 0.050 a, we reject the null hypothesis Since the P-value s a, we reject the null hypothesis. Since the P-value s a, we fail to reject the null hypothesis. e) Interpret your conclusion in the context of the application. At the 5% level of significance, there is insufficient evidence to conclude the variance of annual salaries is greater in Kansas. At the 5% level of significance, there is sufficient evidence to conclude the variance of annual salaries is greater in Kansas. (f) Find the requested confidence interval for the population variance. (Round your answers to two decimal places.) lower limit upper limit5. [0.46/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT 12 10.3.008. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Jim Mead is a veterinarian who visits a Vermont farm to examine prize bulls. In order to examine a bull, Jim first gives the animal a tranquilizer shot. The effect of the shot is supposed to last an average of 65 minutes, and it usually does. However, Jim sometimes gets chased out of the pasture by a bull that recovers too soon, and other times he be random sample of 13 of Jim's bulls had a mean tranquilized duration time of close to 65 minutes but a standard deviation of 26 minutes. At the 1%% level of significance, Is Jim justified in the claim that the variance is larger than that stated in his journal? Find a 95% confidence or should have a mean duration time of 65 minutes, with a standard f 15 minutes. A (a) What is the level of significance? tate the null and alternate hypothe D H,: .' > 225; H,: al - 225 " He: al - 225; H: al > 225 H.: al - 225; H,: al 0.100 D D.050 a, we fail to reject the null hypothesis. D Since the P-value > a, w reject the null hypothesis. Since the F reject the null hypothesis. C) Interpret your conclusion in the context of the application. D At the 19% level of significance, there is Insufficient evidence to co arger than stated in the journal. At the 19% level of significance (f) Find the reg bested confidence Interval for the pop ncard deviation. (Round your ans o decimal place.) lower limit min upper limit 7min6. [0.46/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 10.3.009. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The fan blades on commercial jet engines must be replaced when wear on these parts indicates too much variability to pass inspection. If a single fan blade broke during operation, it could severely endanger a flight. A large engine contains thousands of fan blades, and safety regulations require that variability measurements on the population of all blades not exceed of = 0.18 mm". An engine inspector took a random sample of 61 fan blades from an engine. She measured each blade and found a sample variance of 0.31 mm?. Using a 0.01 level of significance, is the inspector justified in claiming that all the engine fan blades must be replaced? (@) What is the level of significance? State the null and alternate hypotheses. Ho: 02 = 0.18; Hi ? 0.18; H: 0' = 0.18 Ho: 02 = 0.18; H, : > > 0.18 O Ho: 02 = 0.18; H, : 02 # 0.18 b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.) What are the degrees of freedom? What assumptions are you making about the original distribution? O We assume a exponential population distribution. We assume a binomial po on distribution. We assume a uniform population distribution. We assume a normal population distribution. c) Find or estimate the P-value of the sample test statistic. P-value > 0.100 0.050 a, we fail to reject the null hypothesis. Since the P-value > a, we reject the null hypothesis. Since the P-value s a, we reject the null hypothesis. O Since the P-value s a, we fail to reject the null hypothesis. e) Interpret your conclusion in the cont t of the appl O At the 1% level of significance, the evidence urements on the fan blades is higher than the specified amount. The inspector is not justified in claiming the blades must be replaced. At the 1% level of significance, there is ents on the fan blades is higher t mount. The inspector is justified in claiming the blades must be replaced At the 1% level of significance, there is s ents on the fan blades is higher t han the specified amount. The inspector is not justified in claiming the blades must be replaced. O At the 1% level of significance, there is insufficient evidence to conclude that the variance of measurements on the fan blades is higher than the specified amount. The inspector is justified in claiming the blades must be replaced. (f) Find a 90% confidence interval for the population standard deviation. (Round your answers to two decimal places.) lower limit mm upper limit Imm7. [0.4/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 10.3.010. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER fulness of an examination as a measure of demonstrated ability is the amount of spread that occurs in the grades. If the spread or variation of examination scores is very small, it usually means that the examination wes either too hard or too easy. However, if the variance of scores is moderately large, then there is a definite difference in scores between "better," "average," and "poorer" students. A group of attorneys in a Midwest state has been given the task of making up this year's bar examination for the state. The examination has 500 total possible points, and from the history of past examinations, It is known that a standard deviation of around 60 points is desirable. Of course, too large or too small a standard deviation is not good. The attorneys want to test their examination to see how good it is. A preliminary version of the examination (with slight modifications to protect the integrity of the real examination) is given to a random sample of 24 newly graduated law students. Their scores give a sample standard deviation of 66 points. Using a 0.01 level of significance, test the claim that the population standard deviation for the new examination is 60 against the claim that the population standard deviation is different from 60. (a] what is the level of significance? State the null and alternate hypothe O H.: . - 60; H,: D 60; H: 8 - 60 OH,: . - 60; H, : D > 60 b) Find the value of the chi-so trimal places.) what are the degrees of freedom? What assumptions are you making about the original distribution? O We assume a binomial population distribution. O We assume a expo antial population distribution. O We assume a uniform p pulation distribution. We assume a normal population distribution (c) Find or estimate the P-value of the sample test statistic. P-value > 0.100 O D.OSD a, we fail to reject the null hypothesis. O Since the P Since the Puvalue S a, w reject the null hypothesis. Since the Puvalue S a, we fall to reject the null hypothesis (e] Interpret your conclusion in the context of the application At the 1% level of significance, there is in am is different from 60. At the 1% level of signific (f) Find a 99%% confidence interval for the po amal places.) lower limit upper limit (g) Find a 99% confidence interval for the p points Need Help? Pass8. [0.4/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 10.3.011. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A set of solar batteri used in a tellite. The satellite can run on only one battery, but it runs best if more than one battery is used. The variance ad of lifetimes of these Firable for these ba dom sample of 23 batteries gave a sample variance of 15.2 months (squared). Using a D.05 level of significance, test the claim that a? - 23 against the daim that a is different from 23. (a) What is the level of significance? state the null and alternate hypothe OH,: al > 23; H: a - 23 * H,: al - 23; Hj: al + 23 O H,: al - 23; H,: al 23 5) Find the value of the chi-square statistic for t ver to two decimal places.) What are the degrees of freedom? What assumptions are you making about the original distribution? O We assume a exponential population distribution. O We assume a binomial population distribution. We assume a uniform population distribution. c) Find or estimate the P-value of the sample test statistic. P-value > 0.100 O D.050 a, we fall to reject the null hypothesis. Since the P-value > a all hypothesis. Since the Puvalue s a, we reject the null hypothesis. D Since the Puvalue s a, we fall to reject the null hypothesis. c) Interpret your conclusion in the context of the app At the 5% level of significar arent from 23. At the 5% level of significance fe is different from 23. () Find a 90%% confidence Interval for the population variance. (Round your answers to two decimal places.) lower limit upper limit (g) Find a 90%% confidence interval for the popular endmal places.) lower limit months upper limit months Need Help? Rans " Warth