Question

According to a report on workforce diversity, about 60% of the employees in high-tech firms in Silicon Valley are white and about 20% are Asian (http://moneycnn.com, November 9, 2011). Women, along with blacks and Hispanics, are highly underrepresented. Just about 30% of all employees are women, with blacks and Hispanics, accounting for only about 15% of the workforce. Tara Jones is a recent college graduate, working for a large high-tech firm in Silicon Valley. She wants to determine if her firm faces the same diversity as in the report. She collects gender and ethnicity information on 50 employees in her firm. A portion of the data is shown in the accompanying table.

Gender	Ethnicity	Gender	Ethnicity
Female	White	Male	White
Male	White	Female	Nonwhite
Male	Nonwhite	Male	White
Male	White	Male	White
Male	Nonwhite	Female	White
Female	White	Male	White
Male	White	Female	White
Male	White	Male	White
Female	White	Male	Nonwhite
Male	White	Male	Nonwhite
Female	White	Female	White
Male	Nonwhite	Male	Nonwhite
Male	Nonwhite	Female	Nonwhite
Male	Nonwhite	Female	Nonwhite
Female	Nonwhite	Male	White
Male	White	Male	Nonwhite
Female	White	Male	White
Female	Nonwhite	Female	White
Male	White	Male	White
Female	White	Female	Nonwhite
Female	White	Male	White
Male	Nonwhite	Female	Nonwhite
Male	White	Male	White
Male	White	Male	White
Female	White	Male	Nonwhite

At the 5% level of significance, determine if the proportion of non-white employees in Tara’s firm is less than 50%. First, specify the competing hypotheses to test this belief.
	H0: p = 0.50; HA: p ≠ 0.50 H0: p ≥ 0.50; HA: p < 0.50 H0: p ≤ 0.50; HA: p > 0.50

b-2.	Calculate the value of the test statistic. (Round your answer to 2 decimal places.)

Test statistic

  

	The p-value is:
	p-value < 0.01 0.01 ≤ p-value < 0.025 0.025 ≤ p-value < 0.05 0.05 ≤ p-value < 0.10 p-value ≥ 0.10

Answer 1

Solution:

Here, we have to use z test for population proportion.

H₀: p ≥ 0.50

H_A: p < 0.50

This is a lower tailed or left tailed test.

We are given level of significance = α = 0.05

Number of nonwhite employees = x = 18

Total number of employees = n = 50

Sample proportion = P = x/n = 18/50 = 0.36

Calculate the value of the test statistic.

Test statistic formula is given as below:

Z = (P – p)/sqrt(pq/n)

Where, q = 1 – p = 1 – 0.50 = 0.50

Z = (0.36 – 0.50) / sqrt(0.50*0.50/50)

Z = -1.9799

Test statistic = -1.98

P-value = 0.0239

(by using z-table)

0.01 ≤ p-value < 0.025

P-value < α = 0.05

So, we reject the null hypothesis.

There is sufficient evidence to conclude that the proportion of non-white employees in Tara’s firm is less than 50%.