Answer to Question #212603 in Statistics and Probability for Divina Olasiman

Question

Directions:Solve the following real-life problems involving test of hypothesis on the population proportion.State your conclusion.

1. The principal claims that 6 of every 10 learners have access to internet and social networking sites.Upon verification,only 40 out of 70 learners have access to internet and social networking site.At 95% confidence,is the claim true?

2. The health worker claims that less than 30% of COVID-19 cases are asymptomatic.Upon looking at 100 cases,it was found out that 19 of which are asymptomatic.At 99% confidence level,is the claim true?

Answer 1

$H_0:P=0.6$

$H_a:P\ne0.6$

$z=\frac{\hat P-P}{\sqrt{\frac{P(1-P)}{n}}}$

$\hat P=\frac{40}{70}$

$n=70$

$z=\frac{\frac{40}{70}-0.6}{\sqrt{\frac{0.6\times{0.4}}{70}}}$

$=-0.48795$

$CV=z_{0.05}=\pm1.96$ (two-tailed)

Since the absolute value of the test statistic (0.48795) is less than the absolute value of the critical value (1.96), we fail to reject the null hypothesis and conclude that there is enough evidence to support the principal's claim that 6 of every 10 learners have access to internet and social networking sites.

2.

$H_0:P=0.3$

$H_a:P<0.3$

$z=\frac{\hat P-P}{\sqrt{\frac{P(1-P)}{n}}}$

$\hat P=0.19$

$n=100$

$z=\frac{0.19-0.3}{\sqrt{\frac{0.3\times{0.7}}{100}}}$

$=-2.4004$

$CV=z_{0.01}=-2.326$ (left-tailed.)

Since the absolute value of the test statistic (2.4004) is greater than the critical value (2.326), we reject the null hypothesis and conclude that there is enough evidence to support the claim by the health worker that less than 30% of COVID-19 cases are asymptomatic.