Question

After a two-month stay-home order, a poll evaluating support for “multi-stage reopening” in California randomly selected 268 California residents and reported a 60% supportive rate. Carry out a hypothesis test with 5% significance level to check whether a majority of California residents are supportive of the multi-stage reopening.

Write the hypothesis in symbols or words (4 pts)

Check the two conditions for CLT. (2 pts)

Calculate the test statistics (4 pts)

Use the p-value or critical value approach to make your conclusion at 5% significance level. (4 pts)

Answer 1

a)

H0: p = 0.50

Ha: p > 0.50

b)

np = 268 * 0.50 = 134 >= 10

n( 1 - p) = 268 * 0.50 = 134 >= 10

np >= 10 and n(1 - p) >= 10 , so conditions for CLT are satisfied.

c)

Test statistics

z = ( - p) / sqrt [ p ( 1 - p) / n ]

= ( 0.60 - 0.50) / sqrt [ 0.50 ( 1 - 0.50) / 268 ]

= 3.27

d)

p-value = P(Z > z)

= P(Z > 3.27)

= 1 - P(Z < 3.27)

= 1 - 0.9995

= 0.0005

Since p-value < 0.05 level, reject H0

We conclude that there is sufficient evidence to support the claim that a majority of California

residents are supportive of the multi-stage reopening.