In Exercises 1–4, use these results from a USA Today survey in which 510 people chose to respond to this question that was posted on the USA Today website: "Should Americans replace passwords with biometric security (fingerprints, etc)?" Among the respondents, 53% said "yes." We want to test the claim that more than half of the population believes that passwords should be replaced with biometric security.Number and Proportiona. Identify the actual number of respondents who answered "yes."b. Identify the sample proportion and the symbol used to represent it.

Answer:

The proportion of the population believes that passwords should be replaced with biometric security is not more than 50%.

Step-by-step explanation:

In this case we need to test the claim that more than half of the population believes that passwords should be replaced with biometric security.

Assume that the significance level of the test is, α = 0.05.

The hypothesis can be defined as follows:  

H₀: The proportion of the population believes that passwords should be replaced with biometric security is 50%, i.e. p = 0.50.  

Hₐ: The proportion of the population believes that passwords should be replaced with biometric security is more than 50%, i.e. p > 0.50.  

The information provided is:

[tex]n = 510\\\hat p=0.53[/tex]

Compute the test statistic value as follows:

 [tex]z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

    [tex]=\frac{0.53-0.50}{\sqrt{\frac{0.50(1-0.50)}{510}}}\\\\=1.354991\\\\\approx 1.35[/tex]

The test statistic value is 1.35.

The decision rule is:

The null hypothesis will be rejected if the p-value of the test is less than the significance level.

Compute the p-value as follows:

 [tex]p-value=P(Z>1.35)[/tex]

                 [tex]=1-P(Z<1.35)\\=1-0.91149\\=0.08851\\\approx0.088[/tex]

p-value = 0.088 > α = 0.05.

The null hypothesis will not be rejected at 5% significance level.

Thus, there is not enough evidence to support the claim.

Conclusion:

The proportion of the population believes that passwords should be replaced with biometric security is not more than 50%.

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