Answr the following questions 1 Last year 24 percent of the

Answr the following questions

1. Last year 24 percent of the sales and marketing managers at a computer software corporation earned less than $30,000. 15 percent earned at least $30,000 but less than $40,000. 19 percent earned at least $40,000 but less than $50,000, 36 percent earned at least $50,000 but less than $75,000, and 6 percent earned over $75,000. The personnel manager wants to see if there has been a recent change in the distribution of salaries. The following data represent this year\'s salary distribution for a random sample of sales and marketing executives at this company:

Salary

Current Number

Less than $30,000

$30,000 and < $40,000

$40,000 and < $50,000

$50,000 and < $75,000

$75,000 and over

At the .01 level of significance, check to see if there has been a change in the population distribution of salaries at this company.

b. Write the null hypothesis.

b. Write the alternate hypothesis.

c. What is the level of significance?

d. What test must you use to answer this question?

e.What are the degrees of freedom?

f. What is the critical region?

g. State the Decision Rule

h. What is the test ratio?

i. . State the Statistical Decision

2. The sales manager of the Tackey Toy Company has hired a researcher to gather and evaluate opinion data about Tackey products from people in different parts of the country. The researcher randomly sampled toy buyers in each of four regions. Each respondent was first asked if he or she had ever heard of Tackey Toys. Those who were familiar with Tackey products were then asked if Tackey toys were competitively priced or if they were overpriced. The following sample results were obtained:

Geographic Region

Unfamiliar with Tackey Toys

Toys are Priced Competitively

Toys are overpriced

Total

New England

106

198

West Coast

202

Gulf Coast

130

200

Midwest

120

200

Total

264

104

432

800

At the .01 level of significance, check to see if there is no regional differences in the way the population of toy buyers responded to the Tackey survey.

a. Write the null hypothesis.

b. Write the alternate hypothesis.

c. What is the level of significance?

d. What test must you use to answer this question?

e. What are the degrees of freedom?

f. What is the critical region?

g. State the Decision Rule.

h. What is the test ratio?

i. State the Statistical Decision:

Salary	Current Number
Less than $30,000	27
$30,000 and < $40,000	30
$40,000 and < $50,000	30
$50,000 and < $75,000	72
$75,000 and over	57

H0: Distribution is as per last year

Ha: Distribution is not as per last year

Alpha = sign. level = 0.01

d) Chi square test can be used

e) df = 5-1 =4

Prepare contingency table as follows:

p value for chi square 165.1312 for df 4 < 0.00001. The result is significant at p < 0.01.

Hence there is change.

---------------------------------------------

H0: There is no difference between regions for toy purchases

Ha: there is difference

c) sign. level =0.01

d) chi square

e) (r-1)(c-1) = 3(2) = 6

Prepare contingency table for the rest.

chi-square = 39.0
degrees of freedom = 6
probability = 0.000

As p <0.01, reject null hypothesis.

It is statistically evident that there is regional differences in the way the population of toy buyers responded to the Tackey survey.

Salary	Current no	Percent	Expected no	Chi square

<30000	27	24	51.84	11.9025
30000-40000	30	15	32.4	0.177778
	30	19	41.04	2.969825
	72	36	77.76	0.426667
	57	6	12.96	149.6544
	216	100	216	165.1312

Answr the following questions 1. Last year 24 percent of the sales and marketing managers at a computer software corporation earned less than $30,000. 15 percen

Answr the following questions 1 Last year 24 percent of the

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