Question

A researcher believes 20% of all people are left-handed, but you believe it might be less. In a sample of 100 people, 13 people are left-handed. Let p = fraction of left-handed people. You want to test the following:

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Given α = 0.05, what would you conclude?

a) We reject Ho, meaning that proportion of left-handed people is greater than or equal to 20%.

b) We reject Ho, meaning that proportion of left-handed people is less than 20%.

c) We fail to reject Ho, meaning that proportion of left-handed people is greater than or equal to 20%.

d) We fail to reject Ho, meaning that proportion of left-handed people is less than 20%.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.20

H_a : p < 0.20

$\hat p$ = x / n = 13 / 100 = 0.13

1 - P₀ = 0.80

Test statistic = z

= $\hat p$ - P₀ / [$\sqrt$P_{0 *} (1 - P₀ ) / n]

= 0.13 - 0.20 / [$\sqrt$(0.20 * 0.80) / 100]

= -1.75

P(z < -1.75) = 0.0401

P-value = 0.0401

$\alpha$ = 0.05

P-value < $\alpha$

Reject the null hypothesis .

b) We reject Ho, meaning that proportion of left-handed people is less than 20%.