Statistics help! (Hypothesis Testing; z-score)?

Question

I'm very confused for a project, I need to test the hypothesis that the Boston Red Sox are better than the New York Yankees based on a statistic which I chose. The problem is I'm not sure how to set this up. 

μ (Boston) = 108.64
μ (NYY) = 104.17 

so is H0 = μ > 108.64 or μ = 108.64 or μ < 108.64 

Please someone help, I am sorry for not putting this in the best terms but, statistics is obviously very math based. I know how to solve it using the formula (x bar - sample mean/ (standard deviation / square root of n) Just not sure what put as my hypothesis and what to do after finding the z score (-2.94 = .0016) Any help is very appreciated. Thanks!

? · Accepted Answer

The following examples may help.

Testing_difference_2 means in independent populations: z-test

One-tailed-right

Testing for difference of 2 means in independent populations.

Let µ2 be the population mean life of new battery and µ1 be the population mean life of old battery.

H0: µ2-µ1 = 0

H1: µ2-µ1> 0

Sampling involves n1=100, n2=100, large sample sizes

xbar1=190, xbar2=200, s1^2=1600, s2^2=400.

Test Statistics: z-test, z = (200-190)/ √(1600/100 + 400/100) = 2.24

One-tailed test, right, critical region on right tail, of the form {Z>z}

Level of Significance: 0.05

p-value, P{Z>2.24} = P{Z<-2.24} = 0.0125<0.05

Decision: Reject H0 at 0.05. The claim is supported.

Two-tailed

If you are willing to assume independence of spending,

Sample sizes, n1=80, n2=60 large enough,

Xbar~N(µ1, 400/80), Ybar~N(µ2, 900/60)

Let µ2 be the population mean corresponding to seniors and µ1 be the population mean corresponding to freshmen.

H0: µ2-µ1 = 0

H1: µ2-µ1≠ 0

xbar1=340, xbar2=345

Test Statistics: z-test, z = (345-340)/ √ (400/80 + 900/60) = 1.12

Two-tailed test, critical region on both sides, of the form {|Z|>z}.

p-value, P{|Z|>1.12} = 2*P{Z<-1.12} = 2*0.1335 > 0.10

Not significant even at 10%

Conclusion: The claim is not supported.

? · Answer

You are NOT correct.

Ho: Mu1 - Mu2 = 0
Ha: Mu1 > Mu2 (one tailed/right tailed test)
Test statistic = z = (Xbar1 - Xbar2)/SE
SE denotes the standard of error of  the difference between the means
= sqrt (s1^2/n1 + s2^2/n2)
s1^2 denotes the variance of the 1st sample
s2^2 denotes the variance of the 2nd sample
n1 denotes the 1st sample size
n2 denotes the 2nd sample size

Try to find the test statistic (z) and compare with the critical value of z at a particular level of significance and apply the decision rule.

? · Answer

You are not proper. Ho: Mu1 - Mu2 = zero Ha: Mu1 > Mu2 (one tailed/right tailed scan) scan statistic = z = (Xbar1 - Xbar2)/SE SE denotes the common of error of the change between the means = sqrt (s1^2/n1 + s2^2/n2) s1^2 denotes the variance of the 1st sample s2^2 denotes the variance of the 2nd sample n1 denotes the primary sample dimension n2 denotes the 2nd sample size try and find the scan statistic (z) and examine with the enormous price of z at a precise degree of worth and follow the selection rule.

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Statistics help! (Hypothesis Testing; z-score)?

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