Question

Register Balance: Here we investigate whether the register balance at a local retail store is better when a manager is on-duty compared to when a manager is off-duty. Evidence like this might be used to determine whether or not an employee is stealing money from the register when no manager is around. The table below gives the register balance (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) for 10 days when the manager is present and for 10 days when the manager is not present. Test the claim that the mean register balance for all days when the manager is on duty is greater than the mean register balance when the manager is off duty. Test this claim at the 0.01 significance level.

	Manager On Duty	No Manager
count	Register Balance (x1)	Register Balance (x2)
1	-5	2
2	1	-8
3	-7	-15
4	-4	-10
5	5	-10
6	-3	0
7	-2	-12
8	-1	-5
9	-7	0
10	-5	-14
x	-2.80	-7.20
s2	13.96	37.73
s	3.74	6.14

If you are using software, you should be able copy and paste the data directly into your software program.

(a) The claim is that the difference in population means is positive (μ₁ − μ₂ > 0). What type of test is this?

This is a left-tailed test.This is a two-tailed test.    This is a right-tailed test.

(b) Use software to calculate the test statistic or use the formula
t =

(x1 − x2) − δ

s12 n1 + s22 n2

where δ is the hypothesized difference in means from the null hypothesis. Round your answer to 2 decimal places.

t =

To account for hand calculations -vs- software, your answer must be within 0.01 of the true answer.

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places.
P-value =

(d) What is the conclusion regarding the null hypothesis?

reject H₀fail to reject H₀    

(e) Choose the appropriate concluding statement.

The data supports the claim that the mean register balance for all days when the manager is on duty is greater than the mean register balance when the manager is off duty.There is not enough data to support the claim that the mean register balance for all days when the manager is on duty is greater than the mean register balance when the manager is off duty.    We reject the claim that the mean register balance for all days when the manager is on duty is greater than the mean register balance when the manager is off duty.We have proven that someone is stealing money from the register when the manager is not on duty.

Answer 1

(a) The claim is that the difference in population means is positive (μ1 − μ2 > 0). What type of test is this?

This is a right-tailed test.

(b) Use software to calculate the test statistic or use the formula
t = 1.94

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places.
P-value = 0.0367

(d) What is the conclusion regarding the null hypothesis?

fail to reject H0    

(e) Choose the appropriate concluding statement.

There is not enough data to support the claim that the mean register balance for all days when the manager is on duty is greater than the mean register balance when the manager is off duty.    

Register Balance (x1)	Register Balance (x2)
-2.80	-7.20	mean
3.74	6.14	std. dev.
10	10	n
	14	df
	4.400	difference (Register Balance (x1) - Register Balance (x2))
	2.274	standard error of difference
	0	hypothesized difference
	1.94	t
	.0367	p-value (one-tailed, upper)

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