In a newspaper's survey of 442 people, $53.6 \%$ said that we should replace passwords with biometric security, such as fingerprints. The accompanying Statdisk display results from a test of the claim that half of us say that we should replace passwords with biometric security. Use the normal distribution as an approximation to the binomial distribution. Use the display and a 0.05 significance level to complete parts (a) through (e). Sample proportion: 0.5361991 Test Statistic, z: 1.5221 Critical z: \pm 1.9600 P-value: 0.1280 (rrounu to urree uecirnal piaces as neeveo.) d. What is the null hypothesis, and what do you conclude about it? The null hypothesis is $\mathrm{H}_{0}: \mathrm{p} \square \square$, where $\mathrm{p}$ denotes the population proportion of people who say that we should replace passwords with biometric security. $\square$ the null hypothesis. (Type an integer or a decimal. Do not round.)

Step 1 ：The null hypothesis is denoted as \(H_{0}: p = 0.5\), where \(p\) represents the population proportion of people who believe that we should replace passwords with biometric security.

Step 2 ：The test statistic, \(z\), is calculated to be 1.5221.

Step 3 ：The critical \(z\) value at a 0.05 significance level is \(\pm 1.9600\).

Step 4 ：Since the test statistic, \(z = 1.5221\), is less than the critical \(z\) value, we do not reject the null hypothesis.

Step 5 ：The p-value is calculated to be 0.1280, which is greater than the significance level of 0.05. This further supports our decision not to reject the null hypothesis.

Step 6 ：Based on the above analysis, we conclude that there is not enough evidence to reject the null hypothesis that the population proportion of people who say that we should replace passwords with biometric security is 0.5.

Step 7 ：\(\boxed{\text{Final Answer: The null hypothesis is } H_{0}: p = 0.5, \text{ and we do not reject the null hypothesis.}}\)