Question

MP3 Ownership An MP3 manufacturer claims that 65% of teenagers 13 to 16 years old have their own MP3 players. A researcher wishes to test the claim and selects a random sample of 80 teenagers. She finds that 57 have their own MP3 players. At α = 0.05, should the claim be rejected? Use the P-value method.

Answer 1

Solution :

Given that,

$p_{0}$ = 0.65

1 - $p_{0}$ = 0.35

n = 80

x = 57

Level of significance = $\alpha$ = 0.05

Point estimate = sample proportion = $\hat p$ = x / n = 0.71

This a right (One) tailed test.

The null and alternative hypothesis is

Ho: p = 0.65

Ha: p $\neq$ 0.65

Test statistics

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

= ( 0.71 - 0.65) / $\sqrt{}$ (0.65*0.35) / 80

= 1.172

P-value = 2*P(Z>z)

= 2*(1 - P(Z <z ))

= 2*(1- P(Z < 1.172))

= 2*(1 - 0.8794)

= 2*0.1206

= 0.2412

The p-value is p = 0.2412, and since p = 0.2412 > 0.05, it is concluded that the null hypothesis is fail to reject.

Conclusion:

It it is concluded that the null hypothesis is fail to reject. Therefore, there is not enough evidence to claim that the population p

is different than 65% at 0.05 significance level.