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 0.4. You use a significance level of α=0.002α=0.002.

      H0:p=0.4H0:p=0.4
      H1:p≠0.4H1:p≠0.4

You obtain a sample of size n=247n=247 in which there are 92 successes.

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 p-value 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 0.4.
• 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 0.4.
• The sample data support the claim that the proportion of men over 50 who regularly have their prostate examined is different from 0.4.
• 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 0.4.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.4

H_a : p 0.4

= x / n = 92 / 247 = 0.3725

P₀ = 0.4

1 - P₀ = 1-0.40 = 0.60

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.3725 - 0.4 / [0.40*(0.60) /247 ]

= -0.883

P(z <- 0.883 ) = 0.3771

P-value = 0.3771

= 0.002

p= 0.3771 ≥ 0.002, it is concluded that the null hypothesis is not rejected.

Fail to reject the null .

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 0.4.