Below are some questions kindly help me solve

Q.3 An informational collection about speed dating includes? "like" appraisals of male dates made by the female dates. The outline measurements are n=188?, x overbar=7.89?, s=2.05. Utilize a 0.05 importance level to test the case that the populace mean of such appraisals is under 8.00. Expect that a straightforward arbitrary example has been chosen. Distinguish the invalid and alternative? theories, test? measurement, P-worth, and express the last end that tends to the first case.

What are the invalid and alternative? speculations?

Decide the test measurement ___ ?(Round to two decimal spots as? required.)

Decide the? P-esteem ___ ?(Round to three decimal spots as? required.)

Express the last end that tends to the first case.

? Reject, Fail to dismiss H0. There is? not adequate, adequate proof to presume that the mean of the number of inhabitants in evaluations is ? equivalent to, not

more prominent than, under, 8.00.

Settle on a choice about the given case. Utilize just the uncommon event? rule, and make abstract evaluations to decide if occasions are likely. For? model, if the case is that a coin favors heads and test results comprise of 11 heads in 20? flips, reason that there isn't adequate proof to help the case that the coin favors heads? (on the grounds that it is not difficult to get 11 heads in 20 flips by chance with a fair? coin).

?Claim: The mean breath rate left enclosure in breaths each moment right bracket of understudies in a huge math class is more prominent than12.

A basic arbitrary example of the understudies has a mean breath pace of 31.6.

Pick the right answer beneath.

A. The example isn't surprising if the case is valid. The example is strange if the case is false.? Therefore, there isn't adequate proof to help the case.

B. The example is surprising if the case is valid. The example isn't strange if the case is false.? Therefore, there isn't adequate proof to help the case.

C. The example is uncommon if the case is valid. The example isn't uncommon if the case is false.? Therefore, there is adequate proof to help the case.

D. The example isn't strange if the case is valid. The example is uncommon if the case is false.? Therefore, there is adequate proof to help the case.

Information on the weights? (lb) of the substance of jars of diet soft drink versus the substance of jars of the customary form of the soft drink is summed up to one side. Expect that the two examples are autonomous basic arbitrary examples chose from ordinarily distributed? populaces, and don't accept that the populace standard deviations are equivalent. Complete parts? (a) and? (b) beneath. Utilize a 0.05 importance level for the two sections.

a) Test the case that the substance of jars of diet soft drink have loads with an imply that is not exactly the mean for the customary pop.

What are the invalid and alternative? speculations?

The test? measurement, t, is_____.?(Round to two decimal spots as? required.)

The? P-esteem is____. ?(Round to three decimal spots as? required.)

Express the end for the test.

A. Neglect to dismiss the invalid theory. There isn't adequate proof to help the case that the jars of diet soft drink have mean loads that are lower than the mean load for the ordinary pop.

B. Reject the invalid speculation. There is adequate proof to help the case that the jars of diet soft drink have mean loads that are lower than the mean load for the standard pop.

C. Neglect to dismiss the invalid theory. There is adequate proof to help the case that the jars of diet soft drink have mean loads that are lower than the mean load for the customary pop.

D. Reject the invalid theory. There isn't adequate proof to help the case that the jars of diet soft drink have mean loads that are lower than the mean load for the ordinary pop.

b.) Construct a certainty stretch suitable for the theory test in part? (a).

_____ lb

Does the certainty stretch help the end found with the hypothesis? test?

? No,Yes, in light of the fact that the certainty stretch contains ? Zero, Only adverse qualities, Only sure qualities

??

7. Consider the matrix A = ( ] ], ) (a) (10 points) Find the spectral decomposition of A. (b) (10 points) Find an orthogonal matrix P and a diagonal matrix D such that PT AP = D. If {un,...,un} is an orthonormal basis for R" consisting of cigenvectors of A, and Al, ...; An are the corresponding eigenvalues, then the spectral decomposition of A is defined by2.22 Let A = 6 9 4 4 (a) Find the spectral decomposition of A as in (2.109). (b) Find the spectral decomposition of A and show that the diagonal matrix of eigenvalues is equal to the square of the matrix D found in part (a), thus illustrating (2.115). (c) Find the spectral decomposition of A- and show that the diagonal matrix of eigenvalues is equal to the inverse of the matrix D found in part (a), thus illustrating (2.116). 2.23 Find the singular value decomposition of A as in (2.117), where A NAN 2.24 If j is a vector of I's, as defined in (2. 1 1), show that the following hold-h. What's the probability the 3" woman is the 8" person in the sample? i. What's the probability the 3" woman is the 10th person in the sample? J. What's the expected position of the 3" woman in the sample?e. What's the probability fewer than half of the 36 statistics/blostatistics Ph.D.s are women if at least 12 are not women? f. What's the probability the first woman is the 5" person In the sample? g. What's the probability the first woman is the 15" person in the sample