Question

You are conducting a study to see if the accuracy rate for fingerprint identification is significantly different from 0.89. You use a significance level of α=0.05.

      H0:p=0.89
      H1:p≠0.89

You obtain a sample of size n=728 in which there are 672 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) α

• greater than α

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 different from 0.89.
• There is not sufficient evidence to warrant rejection of the claim that the accuracy rate for fingerprint identification is different from 0.89.
• The sample data support the claim that the accuracy rate for fingerprint identification is different from 0.89.
• There is not sufficient sample evidence to support the claim that the accuracy rate for fingerprint identification is different from 0.89.

Answer 1

Solution :

This is the two tailed test .

n = 728

x = 672

= x / n = 672 / 728 = 0.9231

P₀ = 0.89

1 - P₀ = 0.11

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.9231 - 0.89 / [(0.89 * 0.11) / 728]

= 2.852

Test statistic = 2.852

This is the right tailed test .

P(z > 2.852) = 1 - P(z < 2.852) = 0.0022

P-value = 2 * 0.0022 = 0.0044

= 0.05

P-value <

Reject the null hypothesis .

There is sufficient evidence to warrant rejection of the claim that the accuracy rate for fingerprint identification is different from 0.89.