Question

You are conducting a study to see if the accuracy rate for fingerprint identification is significantly more than 0.66. You use a significance level of α=0.001α=0.001.

      H0:p=0.66H0:p=0.66
      H1:p>0.66H1:p>0.66

You obtain a sample of size n=434n=434 in which there are 297 successes.

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

The p-value is...

• less than (or equal to) αα
• greater than αα

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the accuracy rate for fingerprint identification is more than 0.66.
• There is not sufficient evidence to warrant rejection of the claim that the accuracy rate for fingerprint identification is more than 0.66.
• The sample data support the claim that the accuracy rate for fingerprint identification is more than 0.66.
• There is not sufficient sample evidence to support the claim that the accuracy rate for fingerprint identification is more than 0.66.
  You are conducting a study to see if the accuracy rate for fingerprint identification is significantly more than 0.66. You use a significance level of α-: 0.001. Ho:p 0.66 Hi: p0.66 You obtain a sample of size n 434 in which there are 297 successes What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic- What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value The p-value is... O less than (or equal to)a O greater than α This test statistic leads to a decision to... Oreject the null O accept the null O fail to reject the nul
  

Answer 1

Solution :

Given that,

$p_{0}$ = 0.66

1 - $p_{0}$ = 0.34

n = 434

x = 297

Level of significance = $\alpha$ = 0.001

Point estimate = sample proportion = $\hat p$ = x / n = 0.684

This a right (One) tailed test.

Ho: p = 0.66

Ha: p 0.66

Test statistics

z = ($\hat p$ - $p_{0}$ ) / $\sqrt{}$ $p_{0}$*(1-$p_{0}$) / n

= ( 0.684 - 0.66) / $\sqrt{}$ (0.66*0.34) / 434

= 1.055

P-value = P(Z>z)

= 1 - P(Z <z )

= 1- P(Z < 1.055)

= 1 - 0.8543

= 0.1447

The p-value is p = 0.1447, and since p = 0.1447 > 0.001, it is concluded that the null hypothesis is fail to reject.

The p-value is greater than $\alpha$ .

Fail to reject the null hypothesis.