A small appliance company is interested in comparing delivery times of their product during two months. They are concerned that the seasonal slow-downs in August cause delivery times to lag during this month. Given the following delivery times (in days) of their appliances to the customer for a random sample of 6 orders each month, test if delivery times differ across these two months. Assume that the data are nearly normal.

July	52	46	67	68	61	63
August	48	62	73	64	67	73

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Part 1

Which of the following conditions are satisfied for the given data? Select all that apply.

A.

Independence assumption

B.

Independent group assumption

C.

Nearly normal condition

Part 2

Write the null and alternative hypotheses to test if delivery times differ across the two months. Let J correspond to July deliveries and A correspond to August deliveries. Choose the correct answer below.

A.

H0:

JA0;

HA:

JA<0

B.

H0:

JA0;

HA:

JA=0

C.

H0:

JA=0;

HA:

JA0

D.

H0:

JA=0;

HA:

JA<0

Part 3

Find the test statistic.

t=enter your response here

(Round to two decimal places as needed.)

Part 4

Find the P-value.

P=enter your response here

(Round to three decimal places as needed.)

Part 5

Determine a conclusion about the situation. Assume

=0.05.

Choose the correct answer below.

A.

Reject

H0.

The mean delivery time during August is higher, and the difference in delivery time from July is significant. A larger sample may produce a different result.

B.

Reject

H0.

The mean delivery time during August is lower, and the difference in delivery time from July is significant. A larger sample may produce a different result.

C.

Fail to reject

H0.

Thus, although the mean delivery time during July is higher, the difference in delivery time from August is not significant. A larger sample may produce a different result.

D.

Fail to reject

H0.

Thus, although the mean delivery time during July is lower, the difference in delivery time from August is not significant. A larger sample may produce a different result.