Question: Problem 1. To see if there is any significant difference between the average mortgages in the southern (referred to as population 1) and the northern

Problem 1. To see if there is any significant difference between the average mortgages in the southern (referred to as population 1) and the northern California (referred to as population 2), the following information was gathered.

	South (1)	North (2)
Sample Size	40	45
Sample Mean (in $1000)	$170	$175
Sample Standard Deviation (in $1000)	$5	$7

Please answer the following questions (question 1.1 to question 1.10) regarding problem 1 (for dollar value, please use $1000 as unit, i.e., in all your calculation, please directly use the numbers listed in the above table)

Question 1.1. The sample mean difference in problem 1 follows which of the following probability distribution?

Group of answer choices

t distribution

Normal distribution

Binomial distribution

Standard normal distribution

Question 1.2. What is the standard deviation (standard error) of sample mean difference in problem 1? (use $1000 as unit, i.e., the numbers directly from the table)

Question 1.3. What should be the Null hypothesis for problem 1?

Group of answer choices

_1 = _2

_1 _2

Question 1.4. What should be the Alternative hypothesis for problem 1?

Group of answer choices

_1 _2

_1 = _2

_1 _2

Question 1.5. What is the degree of freedom of the distribution for sample mean difference in problem 1?

Question 1.6. What are the test statistics for problem 1? (include sign of the number)

Question 1.7. What is the p-value of the test statistics for problem 1?

Question 1.8. If = 0.05 is used, what is the critical value? (for multiple values, enter the positive one)

Question 1.9. If = 0.05 is used, what is the conclusion of the hypothesis test for problem 1?

Group of answer choices

Fail to reject the Null hypothesis.

Accept the Alternative hypothesis

Reject the Null hypothesis

Fail to reject the Alternative hypothesis

Question 1.10. = 0.05 is used, what is the interpretation of the hypothesis test conclusion in problem 1?

Group of answer choices

There is no significant difference of the average mortgages between Southern and Northern California.

There is a significant difference of the average mortgages between Southern and Northern California.

No answer text provided.

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