Question

(Real data reported in the Boston Globe on 4/11/14) A study by New Jersey-based TD Bank found that out of a sample of 233 couples in Greater Boston, 41 percent maintain separate checking accounts so they can indulge themselves without dipping into the household accounts. The survey found that couples here and across the United States maintain a joint checking account for the obvious household expenses: mortgages, groceries, utilities, and other bills. But when they want to splurge on themselves, for a spa treatment, a daily dose of the venti caramel macchiato at Starbucks, or behind-homeplate seats at a Red Sox game, they spend from their individual accounts. An economist has thought for years that the true proportion of couples keeping separate accounts is actually 35%. What statistics procedure will the economist do with the data? What are the H0 and the Ha for the appropriate hypothesis test? The test produces a P-value of .00001—write a conclusion for the economist.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.35

H_a : p 0.35

n = 233

= 41% = 0.41

P₀ = 0.35

1 - P₀ = 1 - 0.35 = 0.65

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.41 - 0.35 / [(0.35 * 0.65) /233 ]

= 1.92

Test statistic = 1.92

This is the right tailed test .

P(z > 1.92) = 1 - P(z < 1.92) = 1 - 0.9726 = 0.0274

P-value = 2 * 0.0274 = 0.0548