The Congressional Budget Office reports that 36% of federal civilian employees have a bachelor's degree or higher (The Wall Street Journal). A random sample of 115 employees in the private sector showed that 32 have a bachelor's degree or higher. Does this indicate that the percentage of employees holding bachelor's degrees or higher in the private sector is less than in the federal civilian sector? Use α = 0.05. (b) What sampling distribution will you use? What assumptions are you making? The standard normal, since np < 5 and nq < 5. The Student's t, since np > 5 and nq > 5. (inccorect) The Student's t, since np < 5 and nq < 5. (incorrect) The standard normal, since np > 5 and nq > 5. What is the value of the sample test statistic? (Round your answer to two decimal places.) (-1.34, -1.35 is incorrect) (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α? At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. (incorrect) At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (incorrect) At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The Congressional Budget Office reports that 36% of federal civilian employees have a bachelor's degree or higher (The Wall Street Journal). A random sample of 115 employees in the private sector showed that 32 have a bachelor's degree or higher. Does this indicate that the percentage of employees holding bachelor's degrees or higher in the private sector is less than in the federal civilian sector? Use α = 0.05.

(b) What sampling distribution will you use? What assumptions are you making?

The standard normal, since np < 5 and nq < 5.

The Student's t, since np > 5 and nq > 5. (inccorect)

The Student's t, since np < 5 and nq < 5. (incorrect)

The standard normal, since np > 5 and nq > 5.

What is the value of the sample test statistic? (Round your answer to two decimal places.) (-1.34, -1.35 is incorrect)

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. (incorrect)

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (incorrect)

At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.

Expert Solution

Step 1

It is given that out of 115 employees, it is found that 32 have a bachelor’s degree or higher.

The sample proportion is given as

Since both the conditions are satisfied, the normal distribution can be used as the sampling distribution.

Step 2

Since the alternative hypothesis has less than sign, the test is a left-tailed test.

The test statistic is given and calculated as follows.

The left-tailed p-value can be obtained by the Excel formula “=NORM.S.DIST(-1.832,TRUE)”.

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