You would like to construct a 95% confidence interval to estimate the population mean time it takes drivers to react following the application ofbrakes by the driver in front of them. You take a random sample of reaction time measurements and compute their mean to be 1.5 seconds andtheir standard deviation to be 0.4 seconds.(a) What is the best point estimate, based on the sample, to use for the population mean?×(b) For each of the following sampling scenarios, determine which distribution should be used to calculate thecritical value for the 95% confidence interval for the population mean.(In the table, Z refers to a standard normal distribution, and t refers to a t distribution.)secondsSampling scenarioCould useZ tUncleareither Z or tThe sample has size 110, and it is from a non-normallydistributed population with a known standard deviationof 0.45.The sample has size 18, and it is from a normallydistributed population with an unknown standarddeviation.ооооооThe sample has size 20, and it is from a populationwith a distribution about which we know very little.оооооXG

The best point estimate for the population mean is the sample mean. In this case, the sample mean is…

Answered: You would like to construct a 95%…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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You are a researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 35 bacteria reveals a sample mean of ¯x=76x¯=76 hours. The population standard deviation is known to be 5.6 hours. You would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.4 hours at a 90% level of confidence. How many more bacteria should you sample to achieve a 0.4 hour margin of error? n = bacteria
A new screening test for Lyme disease is developed for use in the general population. The sensitivity and specificity of the new test are 60% and 70%, respectively. Five hundred people are screened at a clinic during the first year the new test is implemented. Assume the true prevalence of Lyme disease among clinic attendees is 10%. Calculate the predictive value of a positive test.
A new Economic / Social Conservatism Scale has scores between 0 and 30 (0 being extreme liberal, 30 being extreme conservative). The mean score is 21 and standard deviation of scores is 5. You want to convert the original scale (call it X) to a new scale (call it Y) that has scores between 0 and 100. What is the correlation of X and Y?
Suppose you are working with a data set that is normally distributed, with a mean of 250 and a standard deviation of 46. Determine the value of x from the following information. (a) 70% of the values are greater than x. (b) x is less than 16% of the values. (c) 22% of the values are less than x. (d) x is greater than 55% of the values.
There are many situations in which we want to compare means from populations having standard deviations that are equal. This method applies even if the standard deviations are known to be only approximately equal. Consider a report regarding average incidence of fox rabies in two regions. For region I, n1 = 16, x1 ≈ 4.73, and s1 = 2.84 and for region II, n2 = 15, x2 ≈ 3.93, and s2 = 2.45. The two sample standard deviations are sufficiently close that we can assume ?1 = ?2. Use the method of pooled standard deviation to consider the report, testing if there is a difference in population mean average incidence of rabies at the 5% level of significance. (Round your answer to three decimal places.) t =
A standardized test is given to a sixth-grade class. Historically the mean score has been 151 with a standard deviation of 21. The superintendent believes that the standard deviation of performance may have recently decreased. She randomly sampled 23 students and found a mean of 161 with a standard deviation of 18.2898. Is there evidence that the standard deviation has decreased at the α=0.05 level? Step 1 of 5 : State of the hypotheses in terms of the standard deviation. Round the standard deviation to four decimal places when necessary Step 2 of 5 : Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round your answer to three decimal places. Step 3 of 5 : Determine the value of the test statistic. Round your answer to three decimal places. Step 4 of 5 : Make the decision. Step 5 of 5 : What is the conclusion?
Does buttered toast fall face down? Data was collected to test this. 40 slices of toast (each with butter on one side) were dropped (from the same height). 24 slices (60%) landed buttered side down. We would like to use the results of this study to determine if there is statistical evidence that toast tends to land buttered side down more than 50% of the time.
Deandre is in his first semester at a certain university and is taking a calculus course with a large enrollment. He just took the first midterm exam and is nervous about his score. Among all of the students in the course, the mean of the exam was 67 with a standard deviation of 3. Deandre scored a 62 on this exam. (a) Find the z-score of Deandre's exam score relative to the exam scores among all the students in the course. Round your answer to two decimal places. z=0 (b) Fill in the blanks to interpret the z-score of Deandre's exam score. Make sure to express your answer in terms of a positive number of standard deviations. Deandre's exam score was standard deviations (Choose one) ▼ the mean exam score among all students in the course. Calendar ... 80 F3 F4 F6 F7 F8 F9 F10 F11 云

Foreign freshmen are required to take an English placement exam. Over the past several years, 20% of the new students have failed the test and have been placed in remedial classes. In a sample of n = 100 students from this year’s class, only 12 failed the test.
The lengths of pregnancies in a small rural village are normally distributed with a mean of 267 days and a standard deviation of 15 days.In what range would you expect to find the middle 95% of most pregnancies?Between and .If you were to draw samples of size 55 from this population, in what range would you expect to find the middle 95% of most averages for the lengths of pregnancies in the sample?Between and .

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