91影视

In a survey involving 21346 people, 64% believe that the Loch Ness monster exists. It is claimed that most people believe that the Loch Ness monster exists.

The null hypothesis is written as follows.

The proportion of people who believe that the Loch Ness monster exists is equal to 50%.

$H_0:p=0.5$

The alternative hypothesis is written as follows.

The proportion of people who believe that the Loch Ness monster exists is greater than 50%.

$H_1:p>0.5$

The test is right-tailed.

The sample size is equal to n=21346.

The sample proportion of people who believe that the Loch Ness monster exists is equal to

$$\begin{gathered} \hat{p}=64\% \\ =\frac{64}{100} \\ =0.64 \end{gathered}$$

The population proportion of people who believe that the Loch Ness monster exists is equal to 0.5.

The value of the test statistic is computed below.

$$\begin{gathered} z=\frac{\hat{p}-p}{\sqrt{\frac{pq}{n}}} \\ =\frac{0.64-0.5}{\sqrt{\frac{0.5\left(1-0.5\right)}{21346}}} \\ =40.909 \end{gathered}$$

Thus, z=40.909.

Referring to the standard normal table, the critical value of z at $伪=0.01$ for a right-tailed test is equal to 2.3263.

Referring to the standard normal table, the p-value for the test statistic value of 40.909is equal to 0.000.

As the p-value is less than 0.01, the null hypothesis is rejected.

There is enough evidence to support the claim that the proportion of people who believe that the Loch Ness monster exists is greater than 50%.

If the internet users have chosen to respond to the question, the sample is a voluntary-response sample and cannot be considered a simple random sample.

Thus, the results of the test cannot be relied upon and maybe false.