Question

You are conducting a study to see if the accuracy rate for fingerprint identification is significantly different from 0.47. You use a significance level of α=0.005α=0.005.

      H0:p=0.47H0:p=0.47
      H1:p≠0.47H1:p≠0.47

You obtain a sample of size n=246n=246 in which there are 98 successes.

What is the test statistic for this sample?
test statistic =  (Report answer accurate to 3 decimal places.)

What is the p-value for this sample?
p-value =  (Report answer accurate to 4 decimal places.)

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 different from 0.47.
• There is not sufficient evidence to warrant rejection of the claim that the accuracy rate for fingerprint identification is different from 0.47.
• The sample data support the claim that the accuracy rate for fingerprint identification is different from 0.47.
• There is not sufficient sample evidence to support the claim that the accuracy rate for fingerprint identification is different from 0.47.

Answer 1

Sample proportion = 98 / 246 = 0.3984

Test statistics

z = ( - p ) / sqrt [ p (1 - p ) / n ]

= ( 0.3984 - 047) / sqrt [ 0.47 ( 1 - 0.47) / 246 ]

= -2.250

For two tailed test,

p-value = 2 * P(Z < z)

= 2 * P(Z < -2.250)

= 2 * 0.0122

= 0.0244

p-value is greater than

Decision =

Fail to reject the null

There is not sufficient evidence to warrant rejection of the claim that the accuracy rate for fingerprint identification is different from 0.47