An engineer working for a large agribusiness has developed two types of soil additives he calls Add1 and Add2. The engineer wants to test whether there is anydifference between the two additives in the mean yield of tomato plants grown using these additives.The engineer studies a random sample of 11 tomato plants grown using Add1 and a random sample of 13 tomato plants grown using Add2. (These samples arechosen independently.) The plants grown with Add1 have a sample mean yield of 139 tomatoes with a sample variance of 510. The plants grown with Add2 havea sample mean yield of 151.2 tomatoes with a sample variance of 2178.8.Assume that the two populations of yields are approximately normally distributed. Can the engineer conclude, at the 0.05 level of significance, that there is adifference between the population mean of the yields of tomato plants grown with Add1 and the population mean of the yields of tomato plants grown withAdd2?Perform a two-tailed test. Then complete the parts below.Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.)(a) State the null hypothesis H and the alternate hypothesis H,-Ho : 0H, :0(b) Determine the type of test statistic to use.(Choose one) ▼D=0(c) Find the value of the test statistic. (Round to three or more decimal places.)OO H, :]H, :0(b) Determine the type of test statistic to use.|(Choose one)D=0OSO(c) Find the value of the test statistic. (Round to three or more decimal places.)O

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Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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An engineer working for a large agribusiness has developed two types of soil additives he calls Add1 and Add2. The engineer wants to test whether there is any difference between the two additives in the mean yield of tomato plants grown using these additives. The engineer studies a random sample of 11 tomato plants grown using Add1 and a random sample of 13 tomato plants grown using Add2. (These samples are chosen independently.) The plants grown with Add1 have a sample mean yield of 139 tomatoes with a sample variance of 510. The plants grown with Add2 have a sample mean yield of 151.2 tomatoes with a sample variance of 2178.8. Assume that the two populations of yields are approximately normally distributed. Can the engineer conclude, at the 0.05 level of significance, that there is a difference between the population mean of the yields of tomato plants grown with Add1 and the population mean of the yields of tomato plants grown with Add2? Perform a two-tailed test. Then complete the…
One variety of corn is genetically modified to produce chemicals for defense against predators. The standard corn contains the same standard genotype, but without genetic modification for the chemicals. The two types of corn are then planted in randomly placed adjacent plots across a single field. The amount of predators that are present when the corn has matured are then recorded. The data that was recorded of the predators present among each type are listed. Has genetic alterations decreased the amount of predators for the altered genotype? Normality tests for the populations of both contain a p value less than 0.05. The given alpha is 0.05 Modified Corn (20, 18, 26, 23, 17, 23, 22) Standard Corn (89, 64, 102, 96, 56, 77, 84, 59) use an F test to determine if the variance between the 2 lists are different. Based on this result, state the correct 2 sample parametric test to be used. State the null and alternative. Show calculations while rounding to two decimal points.What is the…
An analysis is performed on vacant land parcels in the city of Thunder Bay to find out whether or not they are randomly distributed. A sample area of 24 square kilometers was studied and divided into quadrats, with the following summary: 3 4 5 3 5 3 Calculate the following statistics: -the mean number of points per cell -the variance: s2 -the variance-to-mean ratio, VMR -the test statistic, x2*Identify the selection below that contains the correct values for these statistics in the same order they are listed. 5.333, 3.37, 2.414, 19.312 24, 9, 1.77, 11.8 3, 2.25, 0.75, 6.0 3.141, 9, 1.893, 15.144 3, 2.25, 1.3333, 10.66
A dietician is researching two new weight gain supplements that have just hit the market: Ripped and Gainz. She wants to determine if there is any difference between the two supplements in the mean amount of weight gained (in kg) by the people who take them. The dietician tracks the total weight gain (in kg) over a year of a random sample of 14 people taking Ripped and a random sample of 12 people taking Gainz. (These samples are chosen independently.) For the people taking Ripped, their sample mean is 10.59 with a sample variance of 6.29. For the people taking Gainz, their sample mean is 9.44 with a sample variance of 1.06. Assume that the two populations of weight gains are approximately normally distributed. Can the dietician conclude, at the 0.10 level of significance, that there is a difference between the population mean of the weights gained by people taking Ripped and the population mean of the weights gained by people taking Gainz? Perform a two-tailed test. Then complete the…
A dietician is researching two new weight gain supplements that have just hit the market: Ripped and Gainz. She wants to determine if there is any difference between the two supplements in the mean amount of weight gained (in kg) by the people who take them. The dietician tracks the total weight gain (in kg) over a year of a random sample of 14 people taking Ripped and a random sample of 12 people taking Gainz. (These samples are chosen independently.) For the people taking Ripped, their sample mean is 10.59 with a sample variance of 6.29. For the people taking Gainz, their sample mean is 9.44 with a sample variance of 1.06. Assume that the two populations of weight gains are approximately normally distributed. Can the dietician conclude, at the 0.10 level of significance, that there is a difference between the population mean of the weights gained by people taking Ripped and the population mean of the weights gained by people taking Gainz? Perform a two-tailed test. Then complete the…
A dietician is researching two new weight gain supplements that have just hit the market: Ripped and Gainz. She wants to determine if there is any difference between the two supplements in the mean amount of weight gained (in kg) by the people who take them. The dietician tracks the total weight gain (in kg) over a year of a random sample of 14 people taking Ripped and a random sample of 12 people taking Gainz. (These samples are chosen independently.) These data are shown in the table. Total weight gains (in kg) Ripped Gainz 14.1, 10.9, 12.1, 5.2, 12.0, 17.1, 9.0, 14.8, 11.2, 6.8, 12.4, 8.5, 12.1, 10.5 Send data to calc... v 7.6, 9.5, 8.6, 10.8, 7.9, 10.0, 8.4, 6.2, 8.6, 10.2, 8.9, 8.2 Send data to Excel Assume that the two populations of weight gains are approximately normally distributed. Can the dietician conclude, at the 0.05 level of significance, that there is a difference between the population mean of the weights gained by people taking Ripped and the population mean of the…
A father is concerned that his teenage son is watching too much television each day, since his son watches an average of 2 hours per day His son says that his TV habits are no different than those of his friends. Since this father has taken a stats class, he knows that can actually test to see whether or not his son is watching more TV than his peers The father collects a random sample of watching times from boys at his son's high school and gets the following data: 1.9, 2.3, 2.2, 1.9, 1.6, 2.6, 1.4, 2.0, 2.0, 2.2 Find a 95% confidence interval for the true mean number of hours teenagers at that school watch TV. a. Confidence Interval b. Conclusion
Tardigrades, or water bears, are a type of micro-animal famous for their resilience. In examining the effects of radiation on arganisms, an expert claimed that the amount of gamma radiation needed to sterilize a colany of tardigrades no longer has a mean of 1200 Gy (grays). (For comparison, humans cannot withstand more than 10 Gy.) A study was conducted on a sample of 21 randomly selected tardigrade colonies, finding that the amount of gamma radiation needed to sterilize a colony had a sample mean af 1225 Gy, with a sample standard deviation of 65 Gy. Assume that the population of amounts of gamma radiation needed to sterilize a colony of tardigrades is approximately normally distributed. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.10 level af significance, to support the claim that H, the mean amount of gamma radiation needed to sterilize a colony of tardigrades, is nat equal to 1200 Gy. (a) State the null hypothesis and the…
ab Tardigrades, or water bears, are a type of micro-animal famous for their resilience. In examining the effects of radiation on organisms, an expert claimed that the amount of gamma radiation needed to sterilize a colony of tardigrades no longer has a mean of 1250 Gy (grays). (For comparison, humans cannot withstand more than 10 Gy.) A random sample of 26 tardigrade colonies found that the amount of gamma radiation needed to sterilize a colony had a sample mean of 1239 Gy, with a sample standard deviation of 45 Gy. Assume that the population of amounts of gamma radiation needed to sterilize a colony of tardigrades is approximately normally distributed. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.10 level of significance, to support that μ, the mean amount of gamma radiation needed to sterilize a colony of tardigrades, is not equal to 1250 Gy. (a) State the null hypothesis Ho and the alternative hypothesis H, that you would use for…
A Chicago-based firm has documents that must be quickly distributed to district offices throughout the U.S. The firm must de- cide between two delivery services, UPX (United Parcel Express) and INTEX (International Express), to transport its documents. In testing the delivery times of the two services, the firm sent two reports to a random sample of its district offices with one report carried by UPX and the other report carried by INTEX. Do the data on the next slide indicate a difference in mean delivery times for the two services? Use a .05 level of significance. [Hint: Perform a hypothesis test for difference for matched/paired samples, D = X1 − X2] (a) State the hypothesis. (b) Decide the significance level. (c) Calculate the test statistic.
A Chicago-based firm has documents that must be quickly distributed to district offices throughout the U.S. The firm must de- cide between two delivery services, UPX (United Parcel Express) and INTEX (International Express), to transport its documents. In testing the delivery times of the two services, the firm sent two reports to a random sample of its district offices with one report carried by UPX and the other report carried by INTEX. Do the data on the next slide indicate a difference in mean delivery times for the two services? Use a .05 level of significance. [Hint: Perform a hypothesis test for difference for matched/paired samples, D = X1 − X2] (d) Find the critical values. (e) Rejection region and conclusion. (f) Interpret the results.
Tardigrades, or water bears, are a type of micro-animal famous for their resilience. In examining the effects of radiation on organisms, an expert claimed that the amount of gamma radiation needed to sterilize a colony of tardigrades no longer has a mean of 1150 Gy (grays). (For comparison, humans cannot withstand more than 10 Gy.) A random sample of 25 tardigrade colonies found that the amount of gamma radiation needed to sterilize a colony had a sample mean of 1133 Gy, with a sample standard deviation of 62 Gy. Assume that the population of amounts of gamma radiation needed to sterilize a colony of tardigrades is approximately normally distributed. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.05 level of significance, to support that u, the mean amount of gamma radiation needed to sterilize a colony of tardigrades, is not equal to 1150 Gy. (a) State the null hypothesis H, and the alternative hypothesis H, that you would use for…

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(a) State the null hypothesis H, and the alternate hypothesis H,. H, :0 H : (b) Determine the type of test statistic to use. (Choose one) ▼ O=0 OSO (c) Find the value of the test statistic. (Round to three or more decimal places.) O