Questions: A survey showed that 34% of human resource professionals are at companies that rejected job candidates because of information found on their social media. If 27 human resource professionals are randomly selected, would 16 be a significantly high number to be at companies that rejected job candidates because of information found on their social media? Why or why not? Select the correct choice below and fill in the answer box within your choice. (Round to four decimal places as needed.) A. Yes, 16 would be significantly high because the probability of 16 or more is , which is not low. B. No, 16 would not be significantly high because the probability of 16 or more is , which is not low. C. No, 16 would not be significantly high because the probability of 16 or more is . which is 1 cx^2 w. D. Yes, 16 would be significantly high because the probability of 16 or more is , which is low.

A survey showed that 34% of human resource professionals are at companies that rejected job candidates because of information found on their social media. If 27 human resource professionals are randomly selected, would 16 be a significantly high number to be at companies that rejected job candidates because of information found on their social media? Why or why not?

Select the correct choice below and fill in the answer box within your choice. (Round to four decimal places as needed.) A. Yes, 16 would be significantly high because the probability of 16 or more is , which is not low. B. No, 16 would not be significantly high because the probability of 16 or more is , which is not low. C. No, 16 would not be significantly high because the probability of 16 or more is . which is 1 cx^2 w. D. Yes, 16 would be significantly high because the probability of 16 or more is , which is low.

Transcript text: A survey showed that $34 \%$ of human resource professionals are at companies that rejected job candidates because of information found on their social media. If 27 human resource professionals are randomly selected, would 16 be a significantly high number to be at companies that rejected job candidates because of information found on their social media? Why or why not? Select the correct choice below and fill in the answer box within your choice. (Round to four decimal places as needed.) A. Yes, 16 would be significantly high because the probability of 16 or more is $\square$ , which is not low. B. No, 16 would not be significantly high because the probability of 16 or more is $\square$ , which is not low. C. No, 16 would not be significantly high because the probability of 16 or more is $\square$ . which is $1 c_{x}^{2} w$. D. Yes, 16 would be significantly high because the probability of 16 or more is $\square$ , which is low.

Solution

Solution Steps

Step 1: Define the Problem

We are tasked with determining whether observing 16 human resource professionals at companies that rejected job candidates due to social media information is significantly high. The probability of a human resource professional being at such a company is $ p = 0.34 $. We randomly select $ n = 27 $ professionals.

Step 2: Calculate the Probability of Exactly 16 Successes

Using the binomial probability formula:

\[ P(X = x) = \binom{n}{x} \cdot p^x \cdot q^{n-x} \]

where $ q = 1 - p = 0.66 $, we find:

\[ P(X = 16) = \binom{27}{16} \cdot (0.34)^{16} \cdot (0.66)^{11} \approx 0.0043 \]

Step 3: Calculate the Cumulative Probability of 16 or More Successes

We compute the cumulative probability for $ X \geq 16 $:

\[ P(X \geq 16) = P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) + P(X = 21) + P(X = 22) + P(X = 23) + P(X = 24) + P(X = 25) + P(X = 26) + P(X = 27) \]

The calculated probabilities for $ X = 17 $ to $ X = 27 $ yield:

\[ P(X \geq 16) \approx 0.0062 \]

Step 4: Determine Significance

To assess whether 16 is significantly high, we compare the cumulative probability $ P(X \geq 16) $ to a significance level, typically $ \alpha = 0.05 $. Since:

\[ P(X \geq 16) \approx 0.0062 < 0.05 \]

we conclude that 16 is indeed a significantly high number.