Question

Based on information from the National Cyber Security Alliance, 93% of computer owners believe that they have antivirus programs installed on their computers. In a random sample of 400 scanned computers, it is found that 380 of them (or 95%) actually have antivirus programs. Use the sample data from the scanned computers to test the claim that 93% of computers have antivirus programs.

 

 

Answer 1

H0: P = 0.93

H1: P ≠ 0.93

 

The test statistic z = (p - P)/sqrt(P(1 - P)/n)

                              = (0.95 - 0.93)/sqrt(0.93 * (1 - 0.93)/400)

                              = 1.57

 

The P-value = 2 * P(Z > 1.57)

                     = 2 * (1 - P(Z < 1.57))

                     = 2 * (1 - 0.9418)

                     = 0.1164

 

As the P-value is greater than the significance level (0.1164 > 0.05), we should not reject H0.

 

So at alpha = 0.05, there is sufficient evidence to support the claim that 93% of computers have antivirus software installed.

So at alpha = 0.05, there is sufficient evidence to support the claim that 93% of computers have antivirus software installed.