# Null and Alternative Hypothesis

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Given a two-tail test for the population mean, the null hypothesis contains a(n) __________ sign, and the alternative hypothesis contains a(n) ___________ sign.

a. ¹, =

b. =, ³

c. £, =

d. =, ¹

Use the following information for questions 3 - 5.

The Waterhole bar and grill decided to run a special offer of a free fried zucchini appetizer with the purchase of a pitcher of beer and a sandwich for Monday nights only during the height of the baseball season. A loyal customer who loves baseball and grows vegetables agreed to supply the squash free. Management's objective was to exceed last year's average Monday night sales volume of $1,900. The data for the 12-week period during the fried zucchini special is as follows:

$2,200 $2,400 $2,100 $2,250$1,800 $1,950 $2,500 $2,600$2,650 $1,600 $2,700 $1,850

Which of the following is/are not an appropriate null hypothesis for a test of the difference between two population means, irrespective of whether the test is one-sided or two-sided?

1. H0: m1 < m

2. H0: m1 > m2

3. H0: m1 ¹ m2

a. 1

b. 2

c. 3

d. 1, 2, and 3

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##### Solution Summary

Given a two-tail test for the population mean, the null hypothesis contains a(n) __________ sign, and the alternative hypothesis contains a(n) ___________ sign.

a. ¹, =

b. =, ³

c. £, =

d. =, ¹

Use the following information for questions 3 - 5.

The Waterhole bar and grill decided to run a special offer of a free fried zucchini appetizer with the purchase of a pitcher of beer and a sandwich for Monday nights only during the height of the baseball season. A loyal customer who loves baseball and grows vegetables agreed to supply the squash free. Management's objective was to exceed last year's average Monday night sales volume of $1,900. The data for the 12-week period during the fried zucchini special is as follows:

$2,200 $2,400 $2,100 $2,250$1,800 $1,950 $2,500 $2,600$2,650 $1,600 $2,700 $1,850

Which of the following is/are not an appropriate null hypothesis for a test of the difference between two population means, irrespective of whether the test is one-sided or two-sided?

1. H0: m1 < m

2. H0: m1 > m2

3. H0: m1 ¹ m2

a. 1

b. 2

c. 3

d. 1, 2, and 3

##### Solution Preview

Solution.(1) Since Two-tailed Test is usually in the form of

<br><br>

<br><br>H0: µ = a

<br><br>H1: µ ¹ a

<br><br>

<br><br> ¹ Means ...

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

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