The mean water temperature downstream from a discharge pipe at a power plant cooling tower should be no more than 100°F. The water temperature is measured on 10 randomly chosen days, and the results are shown below: 96.15 97.81 97.09 95.03 99.46 100.03 99.74 98.85 95.08 98.71 a. State the null hypothesis and alternative hypothesis for the above problem. b. Is there evidence that the water temperature is acceptable at 1% level of significance? c. Find the 95% confidence interval for the mean water temperature. d. Check the results obtained in part b) and c} using Rstudio. Write your conclusion based on the p value obtained in RStudio.
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- A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 197 lb and a standard deviation of 41 lb. The gondola has a stated capacity of 25 passengers, and the gondola is rated for a load limit 3750 . Complete parts (a) through (d) below. a. Given that the gondola is rated for a load limit of 3750 Ib, what is the maximum mean weight of the passengers if the gondola is filled to the stated capacity of 25 passengers? The maximum mean weight is Ib (Type an integer or a decimal. Do not round.) b. If the gondola is filled with 25 randomly selected skiers, what is the probability that their mean weight exceeds the value from part (a)? The probability is (Round to four decimal places as needed.) filled with 20 randomly selected skiers, what is the probability that their mean weight exceeds 187.5 lb, which is the maximum mean c. If the weight assumptions were revised so that the new capacity became 20 passengers and the gondola…According to United States Department of Agriculture, the average retail price of conventional whole milk at New York City in the year 2020 (up to November 2020 considered) is $3.92 per gallon. The standard deviation in the retail prices in the year 2020 (up to November 2020 considered) is $0.084. You are given a task of selecting randomly a sample of 85 milk bottles (whole milk of 1 gallon volume). a. Calculate µx̅ and σx̅. b. What is the approximate probability that the sample has a mean retail price that exceeds $4.05? c. What is the approximate probability that the sample has a mean retail price between $3.91 and $3.94?A boat capsized and sank in a lake. Based on an assumption of a mean weight of 133 Ib, the boat was rated to carry 70 passengers (so the load limit was 9,310 Ib). After the boat sank, the assumed mean weight for similar boats was changed from 133 lb to 174 lb. Complete parts a and b below. a. Assume that a similar boat is loaded with 70 passengers, and assume that the weights of people are normally distributed with mean of 181.1 Ib and a standard deviation of 38.6 lb. Find the probability that the boat is overloaded because the 70 passengers have mean weight greater than 133 lb The probability isO: (Round to four decimal places as needed.) b. The boat was later rated to carry only 17 passengers, and the load limit was changed to 2,958 Ib. Find the probability that the boat is overloaded because the mean weight of the passengers is greater than 174 (so that their total weight is greater than the maximum capacity of 2,958 Ib). The probability is. (Round to four decimal places as needed.)…
- A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 180 lb and a standard deviation of 36 lb. The gondola has a stated capacity of 25 passengers, and the gondola is rated for a load limit of 3500 lb. Complete parts (a) through (d) below. a. Given that the gondola is rated for a load limit of 3500 lb, what is the maximum mean weight of the passengers if the gondola is filled to the stated capacity of 25 passengers? The maximum mean weight is 140 lb. (Type an integer or a decimal. Do not round.) b. If the gondola is filled with 25 randomly selected skiers, what is the probability that their mean weight exceeds the value from part (a)? The probability is: (Round to four decimal places as needed.)A water taxi carries passengers from harbor to another. Assume that weights of passengers are normally distributed with a mean of 185 lb and a standard deviation of 39 lb. The water taxi has a stated capacity of 25 passengers, and the water taxi was rated for a load limit of 3500 lb. Complete parts (a) through (d) below. a. Given that the water taxi was rated for a load limit of 3500 lb, what is the maximum mean weight of the passengers if the water taxi is filled to the stated capacity of 25 passengers? The maximum mean weight is lb. (Type an integer or a decimal. Do not round.) b. If the water taxi is filled with 25 randomly selected passengers, what is the probability that their mean weight exceeds the value from part (a)? The probability is (Round to four decimal places as needed.) c. If the weight assumptions were revised so that the new capacity became 20 passengers and the water taxi is filled with 20 randomly selected passengers, what is the probability that their mean weight…A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 197 lb and a standard deviation of 43 lb. The gondola has a stated capacity of 25 passengers, and the gondola is rated for a load limit of 3750 Ib. Complete parts (a) through (d) below. a. Given that the gondola is rated for a load limit of 3750 lb, what is the maximum mean weight of the passengers if the gondola is filled to the stated capacity of 25 passengers? The maximum mean weight is Ib. (Type an integer or a decimal. Do not round.) b. If the gondola is filled with 25 randomly selected skiers, what is the probability that their mean weight exceeds the value from part (a)? The probability is (Round to four decimal places as needed.) c. If the weight assumptions were revised so that the new capacity became 20 passengers and the gondola is filled with 20 randomly selected skiers, what is the probability that their mean weight exceeds 187.5 lb, which is the…
- Each observation in a random sample of 98 bicycle accidents resulting in death was classified according to the day of the week on which the accident occurred. Data consistent with information are given in the following table. x² Day of Week Frequency = Sunday Monday Tuesday Wednesday Thursday Friday Saturday 13 12 12 14 13 18 Based on these data, is it reasonable to conclude that the proportion of accidents is not the same for all days of the week? Use a = 0.05. Calculate the test statistic. (Round your answer to two decimal places.) 16 Use technology to calculate the P-value. (Round your answer to four decimal places.) P-value = State the conclusion in the problem context. O Reject Ho. We have convincing evidence that the proportion of accidents is not the same for all days of the week. O Fail to reject Ho. We have convincing evidence that the proportion of accidents is not the same for all days of the week. ● Fail to reject Ho. We do not have convincing evidence that the proportion…A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 186 lb and a standard deviation of 44lb. The gondola has a stated capacity of 25 passengers, and the gondola is rated for a load limit of 3500lb. Complete parts (a) through (d) below. A. Given that the gondola is rated for a load limit of 3500lb, what is the maximum mean weight of the passengers if the gondola is filled to the stated capacity of 25 passengers? The maximum mean weight is______ B. If the gondola is filled with 25 randomly selected skiers, what is the probability that their mean weight exceeds the value from part (a)? The probability is____ C. If the weight assumptions were revised so that the new capacity became 20 passengers and the gondola is filled with 20 randomly selected skiers, what is the probability that their mean weight exceeds 186 lb, which is the maximum mean weight that does not cause the total load to exceed 3500lb? The…A paper investigated the driving behavior of teenagers by observing their vehicles as they left a high school parking lot and then again at a site approximately mile from the school. Assume that it is reasonable to regard the teen drivers in this study as representative of the population of teen drivers. Amount by Which Speed Limit Was Exceeded Female Driver -0.1 0.4 1.1 0.7 1.1 1.2 0.1 0.9 0.5 0.5 (a) Use a .01 level of significance for any hypothesis tests. Data consistent with summary quantities appearing in the paper are given in the table. The measurements represent the difference between the observed vehicle speed and the posted speed limit (in miles per hour) for a sample of male teenage drivers and a sample of female teenage drivers. (Use males - females: Round your test statistic to two decimal places. Round your degrees of freedom down to the nearest whole number. Round your p-value to three decimal places.) t= df = P = Male Driver 1.4 1.2 0.9 2.1 0.7 1.3 3 1.3 0.6 2.1 (b) Do…
- Refer to the figure at the right. At a= 0.10, can you reject the claim that the proportion of 18 to 24-year-olds living in their parents' homes in 2000 was the same for men and women? Assume the survey included a random sample of 270 men and 278 women. Percentage of 18- to 24-year olds living in parents' homes 70, 60.4% 45% 54.6% 50.3% 2000 2012 Men Women Identify the null and alternative hypotheses. Choose the correct answer below. O B. Ho: P, * P2 Ha: P1 = P2 OD. Ho: P1 > P2 YA. Ho: P1 = P2 H3: P, * P2 OC. Ho: P, P2 Ha: P, SP2 Find the critical value(s). The critical value(s) is(are). (Round to two decimal places as needed. Use a comma to separate answers as needed.)Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 48 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that σ = 8.00 ml/kg for the distribution of blood plasma. When finding an 99% confidence interval, what is the critical value for confidence level? (Give your answer to two decimal places.) Z=0.005 (a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.) lower limit upper limit margin of error (b) What conditions are necessary for your calculations? (Select all that apply.) the distribution of volumes is normal ✔ is known o is unknown the distribution of volumes is…A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 182 lb and a standard deviation of 38 lb. The gondola has a stated capacity of 25 passengers, and the gondola is rated for a load limit of 3500 lb. Complete parts (a) through (d) below. a. Given that the gondola is rated for a load limit of 3500 Ib, what is the maximum mean weight of the passengers if the gondola is filled to the stated capacity of 25 passengers? The maximum mean weight is Ib. (Type an integer or a decimal. Do not round.) b. If the gondola is filled with 25 randomly selected skiers, what is the probability that their mean weight exceeds the value from part (a)? The probability is. (Round to four decimal places as needed.) c. If the weight assumptions were revised so that the new capacity became 20 passengers and the gondola is filled with 20 randomly selected skiers, what is the probability that their mean weight exceeds 175 lb, which is the…