Question

1. Based on information from the National Cyber Security Alliance, 93 % of computers 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 actually have antivirus programs. Test the claim that 93% of computers have antivirus programs using the p-value approach.

Answer 1

Given that, n = 400 and x = 380

=> sample proportion = 380/400 = 0.95

The null and alternative hypotheses are,

H0 : p = 0.93

Ha : p ≠ 0.93

This hypothesis test is a two-tailed test.

Test statistic is,

=> Test statistic = Z = 1.57

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

=> p-value = 2 * [ 1 - P(Z < 1.57) ]

=> p-value = 2 * [ 1 - 0.9418 ]

=> p-value = 2 * 0.0582

=> p-value = 0.1164

Since, p-value is greater than 0.05 level of significance, we fail to reject the null hypothesis (H0).

Conclusion : There is not sufficient evidence to warrant rejection of the claim that 93% of computers have antivirus programs.