Question

A new engineering software is being developed and claim that it is more than 98% compatible with the existing software. A sample of 200 engineering firms tested the new software and 180 of them agreed with the manufacturer. Test at 5% significance level whether the claim is true

Answer 1

$Null\;Hypothesis\;H_0:\;p=0.98.\\ Alternative\;Hypothesis\;H_a:\;p>0.98.\\ Test\;statistic:\;z=\frac{\frac{180}{200}-0.98}{\sqrt{\frac{0.98*(1-0.98)}{200}}}=-8.08.\\ P-value:\;p=1.000.\\ Since\;the\;P-value\;is\;greater\;than\;0.05,\;fail\;to\;reject\;the\;null\;hypothesis.\\ The\;claim\;is\;not\;true.$