Many properties of the fabric used in different textiles, such as sheets and clothing, are influenced by whether the diameter of yarn used in the creation of the textile is consistent. Therefore, various methods can be used to measure the diameter of yarn at specified intervals, such as every 2mm, to determine the consistency of the diameter. These measurements are normally distributed. Suppose that one textile manufacturer will not use any yarn in which the variance of the diameters is greater than 0.0009mm. In order to ensure that the yarn is usable, the diameter of a length of yarn is measured at 400 random intervals. The variance of those measurements is found to be 0.000992mm. Does this evidence provide support that the batch of yarn is unusable by the manufacturer? Use a 0.005 level of significance.   Step 2 of 3 :   Compute the value of the test statistic. Round your answer to three decimal places.

.The two data sets below represent the high temperatures in two citieseach day for 5 days.City A: 18°F, 44°F, 52°F, 55°F, 58°F, 56°FCity B: 15°F, 41°F, 63°F, 61°F, 57°F, 60°F Which statementbestdescribes the measure of center that provides themost accurate estimation of the high temperature in a day in each city? A.mean, because there is an even number of values in each data set B.median, because there is an even number of values in each data set C.mean, because there is one value in each data set that is significantlylower than the other values D.median, because there is one value in each data set that issignificantly lower than the other values

Psi is a measure of compressive strength, or the ability of the material to carry loads and handle compression. The desired concrete psi rating used for sidewalks and residential driveways ranges from 2500psi to 3000psi obtained from mixing cement, stone, and sand in different ratios but with the same amount of water. The summary of the psi's of three (3) such concrete mixes made by three (3) different civil engineering students is given as follows: Mean vector: The variance-covariance matrix: Concrete mix Mean Concrete mix 1 Concrete mix 2 Concrete mix 3 Concrete mix 1 | Concrete mix 2 2700 18 12 2 3000 12 16 3 2400 Concrete mix 3 16 25 Let the random variable Y be the vector of the psi's of concrete mixes obtained by the students, i.e. Y1, denotes the psi of concrete mix made by student 1, Y2 is the psi of concrete mix made by student 2 and Y3 is the psi of concrete mix psi made by student 3. (a) Find (i) the multivariate probability distribution function (pdf) of Y. (ii) the…

4. In a study, researchers wanted to measure the effect of alcohol on the hippocampal region, the portion of the brain responsible for long-term memory storage, in adolescents. The researchers randomly selected 21 adolescents with alcohol use disorders to determine whether the hippocampal volumes in the alcoholic adolescents were less than the normal volume of 9.02 cm°. An analysis of the sample data revealed that the hippocampal volume is approximately normal with no outliers and x = 8.14 cm ands = 0.8 cm³. Conduct the appropriate test at the a = 0.01 level of significance. State the null and alternative hypotheses. Ho: H (1) H1: µ (2) (Type integers or decimals. Do not round.) Identify the t-statistic. to = (Round to two decimal places as needed.) Identify the P-value. P-value = (Round to three decimal places as needed.) Make a conclusion regarding the hypothesis. (3) the null hypothesis. There (4) sufficient evidence to claim that the mean hippocampal volume is (5) cm³. 3

A manufacturing company produces bearings. One line of bearings is specified to be 1.64 centimeters (cm) in diameter. A major customer requires that the variance of the bearings be no more than .001 cm². The producer is required to test the bearings before they are shipped, and so the diameters of 16 bearings are measured with a precise instrument, resulting in the following values. Assume bearing diameters are normally distributed. Use the data and a = 0.01 to test to determine whether the population of these bearings is to be rejected because of too high a variance. 1.68 1.62 1.63 1.70 1.66 1.63 1.65 1.71 1.64 1.69 1.57 1.64 1.59 1.66 1.63 1.65 Appendix A Statistical Tables (Round your answer to 2 decimal places, e.g. 15.25.) The value of the test statistic is and we reject the null hypothesis ⇒

A. 2.1