Question

A statistics professor asked his class to use the following chart to first, determine what statistic method should be used. Two, answer the following information: Step 1: State the point estimate Step Two: State the null and alternative hypothesis Step 3: Label a diagram with the approperiate tails and critical values Step 4: Calculate the test statistics, Step five: State the conclusion

How does one's high school grade point adverage affect the potential earning for males and females?

High School GPA Males & Total Number of Males	High School GPA & Total Number of Females	Average Yearly Income Male and Female
GPA:4.0 Total: 1	GPA: 4.0            Total 3	Male: $65,000 Female: $54,000
GPA: 3.5 Total: 5	GPA: 3.5 Total: 7	Male: $55,000 Female: $48,000
GPA:3.0 Total: 6	GPA: 3.0 Total: 4	Male: $42,000 Female: $36,000
GPA: 2.5 Total:2	GPA: 2.5 Total: 2	Male: $35,000 Female: $27,000
GPA:2.0 Total:1	GPA: 2.0 Total: 2	Male: $23,000 Female: $18,000
GPA:1.5 Total:3	GPA: 1.5 Total: 1	Male: $20,000 Female: 14,000
GPA:1.0 Total: 1	GPA: 1.0 Total: 1	Male: $18,000 Female: $9,000
GPA:0.5 Total: 0	GPA: 0.5 Total: 0	No Data
GPA: 0.0 Total: 0	GPA: 0.0 Total: 0	No Data

Answer 1

First, clean the data and write in the table format:

GPA	Male count	Female count	Male income	Female income
4.0	1	3	65000	54000
3.5	5	7	55000	48000
3.0	6	4	42000	36000
2.5	2	2	35000	27000
2.0	1	2	23000	18000
1.5	3	1	20000	14000
1.0	1	1	18000	9000

1) Point Estimates:

From the above bar diagram, the female is got more GPA score than the male.

The average income of Male is $36,857

The average income of Female is $29,428

i.e. Male earning is higher than the female for same GPA scorer.

Hypothesis Testing:

H0: The average earning of Male and Female is same for same GPA group. (1 = 1)

against,

H1: The average earning of Male and Female is different for the same GPA group.

(1 != 1)

Test Statistics:

for identifying the difference in the two mean group we want to use t-test here.

by using the R:

> t.test(Male_income,Female_income)

Welch Two Sample t-test

t = 0.78443, df = 11.967, p-value = 0.448

alternative hypothesis: true difference in means is not equal to 0

95 percent confidence interval:

( -13211.11 , 28068.26 )

sample estimates:

mean of x mean of y

36857.14 29428.57

From the above output:

t statistic = 0.78443

p-value = 0.448

Decision Rule:
If the p-value is greater than the level of significance(0.05) then we accept the null hypothesis
otherwise, reject the null hypothesis.

p-value 0.448 > 0.05

i.e. we accept the null hypothesis.

i.e.The average earning of Male and Female is same for same GPA group.

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