Question

An incumbent city official was running for another term. She was interested in determining whether the percentage of registered voters favoring her candidacy had increased since the last election. At that time, 52% of the registered voters favored her candidacy. A simple random sample of 500 registered voters showed that 270 favored her. Do the data provide sufficient evidence to favor the null hypothesis? Perform an appropriate hypothesis test.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.52

H_a : p >0.52

n = 500

x = 270

= x / n = 270 / 500 = 0.54

P₀ = 0.52

1 - P₀ = 1 - 0.52 = 0.48

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.54 - 0.52 / [(0.52 * 0.48) / 500]

= 0.895

Test statistic = 0.895

P(z > 0.895) = 1 - P(z < 0.895) = 1 - 0.8146 = 0.1854

P-value = 0.1854

= 0.05

P-value >

Fail to reject the null hypothesis .

The data does provide sufficient evidence to favor the null hypothesis .

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.52

H_a : p >0.52

n = 500

x = 270

= x / n = 270 / 500 = 0.54

P₀ = 0.52

1 - P₀ = 1 - 0.52 = 0.48

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.54 - 0.52 / [(0.52 * 0.48) / 500]

= 0.895

Test statistic = 0.895

P(z > 0.895) = 1 - P(z < 0.895) = 1 - 0.8146 = 0.1854

P-value = 0.1854

= 0.05

P-value >

Fail to reject the null hypothesis .

The data does provide sufficient evidence to favor the null hypothesis .