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How do I find the p value? Please explain in detail
Previous Problem Problem List Next Problem 1 polnt) Here we Investigate whether the register balance at a local retail store is better on days with a manager than days without a manager. This evidence might be used to determine whether or not you should always schedule a manager. The table gives the register balance for a sample of 10 days with a manager and 10 days without a manager. Here, 0 means the register balance is right on, negative means there is less money than there should be, and positive means there is more money than there should be. The number of degrees of freedom (d.1.) that you should use in your calculations is glven in the table. Register Balance (10 days each) mean With Manager (x1) 4 4 0 3 1 0 -4 0 1 0 1.5 4.05555555555556 2.0138409955991 Without Manager (x2) -17 -10 -8 -5 8 3 4 25 0 1 8.1 59.6555555555556 7.72370089759796 degrees of freedom: d.f.-10 Test the claim that the average register balance is better (greater) for all days with a manager than those days without a manager. Use a 0.01 significance level (a) Find the test statistic (to 3 decimal places) 26148 (b) Find the P value to 3 decimal places) 0.9871 (c) Is there sufficient data to support the claim? Yes O No d) Test the same claim at the 0.05 significance level. iIs there sufficient data to support the claim? O Yes No Note: You can eam partial credit on this problem Preview My Answers Submit Answers You have attempted this problem 2 tmes Your overall recorded score is 75%.
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The following null and alternative hypotheses need to be tested This corresponds to a right-tailed test, for which a t-test for two population means, with two independent samples, with unknown population standard deviations will be used (2) Rejection Region Based on the information provided, the significance level is α 0.01, and the degrees of freedom are df 10.218. In fact, the degrees of freedom are computed as follows, assuming that the population variances are unequal Hence, it is found that the critical value for this right-tailed test is t df-10218 2.753, for a 0.01 and The rejection region for this right-tailed test is R- It:t>2.753 (3)_Test Statistics Since it is assumed that the population variances are unequal, the t-statistic is computed as follows (n1-1)s2+(n2-1)s1 712 1.5--8.1 2.615 (10-12.0138409992+(10-1)7.72370089759 (1 1 1 10+10-2 10 10 he null hypothesis Since it is observed that t-2.615 < tcー2.753, it is then concluded that the null hypothesis is not rejected Using the P-value approach: The p-value is p 0.0127, and since p-0.0127 > 0.01, it is concluded that the null hypothesis is not rejected

a)

TS = 2.615

b)

p-value = 0.0127

c)

p-value < alpha (0.01)

Yes

d)

Yes

as p-value < 0.01

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