Question

PLEASE ANSWER ALL PARTS!

Various studies indicate that approximately 9% of the world's population is left handed. You think this number is actually higher. You take an SRS of 222 people and find that 23 of them are left handed. Test your claim at the 5% significance level.

Part a: State your null and alternative hypotheses.

Part b: State the rejection region.

Part c: Calculate the test statistic.

Part d: Determine the P-value for your test.

Part e: State your conclusion for your hypothesis test.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H0 : p = 0.09

Ha : p > 0.09

= x / n = 23/222 = 0.1036

P0 = 0.09

1 - P0 = 1-0.09 = 0.91

= 0.05

The right tailed test critical value is zc = 1.645

z > 1.645

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

=0.1036-0.09 / [0.09*(0.91) /222 ]

= 0.708

P(z > 0.708) = 1 - P(z <0.708 ) = 0.2395

P-value = 0.2395

= 0.05

0.2395 >  0.05

Do not reject the null hypothesis .

There is insufficient evidence to suggest that