Question

You are conducting a study to see if the proportion of men over 50 who regularly have their prostate examined is significantly different from 0.6. You use a significance level of α=0.005α=0.005.

      H0:p=0.6H0:p=0.6
      H1:p≠0.6H1:p≠0.6

You obtain a sample of size n=489n=489 in which there are 262 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 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 proportion of men over 50 who regularly have their prostate examined is different from 0.6.
• There is not sufficient evidence to warrant rejection of the claim that the proportion of men over 50 who regularly have their prostate examined is different from 0.6.
• The sample data support the claim that the proportion of men over 50 who regularly have their prostate examined is different from 0.6.
• There is not sufficient sample evidence to support the claim that the proportion of men over 50 who regularly have their prostate examined is different from 0.6.

Answer 1

Sample proportion = 262 / 489 = 0.5358

Test statistics

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

= ( 0.5358 - 0.6) / sqrt ( 0.6 ( 1 - 0.6) / 489 )

= -2.898

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

= 2 * P ( Z < -2.898)

= 2 * 0.0019

= 0.0038

The p-value is less than .

This test statistic leads to a decision to

reject the null

There is sufficient evidence to warrant rejection of the claim that the proportion of men over 50 who regularly have their prostate examined is different from 0.6.