the actual dose administered is normally distributed with mean μ mg and variance σ 2 = 2.6 mg2.
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Medication used to treat a certain condition is administered by syringe. The target dose in a particular application is μ. Because of the variations in the syringe, in reading the scale, and in mixing the fluid suspension, the actual dose administered is
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- You are thinking about opening a restaurant and are searching for a good location. From research you have done, you know that the mean income of those living near the restaurant must be over $85,000 to support the type of upscale restaurant you wish to open. You decide to take a simple random sample of 50 people living near one potential location. Based on the mean income of this sample, you will perform a test of Ho : μ = $85,000 Haμ> $85,000 where is the true mean income in the population of people who live near the restaurant. Which of the following is not true regarding Type I and Type II errors in this setting? All of these statements are true. A possible consequence of a Type I error here is you may open your restaurant in a location where the residents will not be able to support it, so your restaurant may go out of business. A Type I error occurs when you find convincing evidence that the mean income of all residents near the restaurant exceeds $85,000 when in reality it does…A notable indicator of a baby's health is the weight gained in the first year of the baby's life. Assume that the population of all such weight gains for baby boys is approximately normally distributed. A study claimed that the mean of this population is 4.93 kg. As a practicing pediatrician, you want to test this claim. So, you select a random sample of 16 baby boys, and you record the weight each gained in their first year. Follow the steps below to construct a 99% confidence interval for the population mean of all the weight gains for baby boys in their first year. Then state whether the confidence interval you construct contradicts the study's claim. (If necessary, consult a list of formulas.) (a) Click on "Take Sample" to see the results for your random sample. Sample standard Number of baby boys Sample mean deviation Take Sample 16 5.496 1.873 Enter the values of the sample size, the point estimate of the mean, the sample standard deviation, and the critical value you need for…A pharmaceutical company makes tranquilizers. It is assumed that the distribution for the length of time they last is approximately normal. Researchers in a hospital used the drug on a random sample of 9 patients. The effective period of the tranquilizer for each patient (in hours) was as follows: 2.6; 2.8; 3.0; 2.3; 2.3; 2.2; 2.8; 2.1; and 2.4.NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) (i) Round your answer to two decimal places. x = (rounded to two decimal places)(ii) Round your answer to two decimal places. sx = (rounded to two decimal places)(iii) Enter an exact number as an integer, fraction, or decimal. n = (iv) Enter an exact number as an integer, fraction, or decimal. n − 1 = Which distribution should you use for this problem? (Enter your answer in the form z or tdf where df is the degrees of freedom.)
- A pharmaceutical company makes tranquilizers. It is assumed that the distribution for the length of time they last is approximately normal. Researchers in a hospital used the drug on a random sample of 9 patients. The effective period of the tranquilizer for each patient (in hours) was as follows: 2.6; 2.8; 3.0; 2.3; 2.3; 2.2; 2.8; 2.1; and 2.4.NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Part (a)The acceptable level for insect filth in a certain food item is 2insect fragments (larvae, eggs, body parts, and so on) per 10 grams. A simple random sample of 50 ten-gram portions of the food item is obtained and results in a sample mean of x=2.5 insect fragments per ten-gram portion. Complete parts (a) through (c) below.If Y is Normally distributed , and p(y < 170 ) = 0.14 p ( y > 200 ) = 0.03 then the values of the mean and variance of Y , respectively are
- A pharmaceutical company makes tranquilizers. It is assumed that the distribution for the length of time they last is approximately normal. Researchers in a hospital used the drug on a random sample of 9 patients. The effective period of the tranquilizer for each patient (in hours) was as follows: 2.5; 2.9; 3.1; 2.3; 2.3; 2.2; 2.8; 2.1; and 2.4.Data Table Type A 7.3 7.6 7.1 7.1 7.1 7.9 6.4. 6.9 7.5 7.2 Type B 8.7 8.2 8.3 7.7 8.8 8.2 8.7 7.1 Type С 8.5 8.3 9.3 9.2 9.3 9.5 8.8 8.7 8.5 - XOur environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 7.9 parts/million (ppm). A researcher believes that the current ozone level is at an excess level. The mean of 24 samples is 8.1 ppm with a variance of 0.25. Does the data support the claim at the 0.1 level? Assume the population distribution is approximately normal. Step 5 of 5: Make the decision to reject or fail to reject the null hypothesis.
- The distribution of male height (X) in the US is known to be normally distributed with mean of about 70 inches and variance of 25 inches. What is the IQR? (hint: think about what the IQR represents in a boxplot with regard to percentiles). The z tables can be found at the bottom of the written portion of the exam or at the end of Lecture Note 10. a.) 5.0 b.) 9.0 c.) 7.3 d.) 10.0 e.) 6.7Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 4.6 parts/million (ppm). A researcher believes that the current ozone level is at an excess level. The mean of 14 samples is 4.9 ppm with a variance of 1.2 Does the data support the claim at the 0.01 level? Assume the population distribution is approximately normal. Step 2 of 5 : Find the value of the test statistic. Round your answer to three decimal places.The director of research and development is testing a new drug. She wants to know if there is evidence at the 0.02 level that the drug stays in the system for more than 312 minutes. For a sample of 69 patients, the mean time the drug stayed in the system was 319 minutes. Assume the variance is known to be 400. Step 2 of 5 : Enter the value of the z test statistic. Round your answer to two decimal places.
