Question

A cell phone company offers two plans to its subscribers. At the time new subscribers sign up, they are asked to provide some demographic information. The mean yearly income for a sample of 38 subscribers to Plan A is $58,500 with a standard deviation of $8,000. This distribution is positively skewed; the coefficient of skewness is not larger. For a sample of 42 subscribers to Plan B, the mean income is $59,100 with a standard deviation of $9,500. At the 0.02 significance level, is it reasonable to conclude the mean income of those selecting Plan B is larger?

a. State the decision rule. (Negative answer should be indicated by a minus sign. Round the final answer to 3 decimal places.)

Reject H0 if t > _________ -1.665 Incorrect.

b. Compute the value of the test statistic. (Negative answer should be indicated by a minus sign. Round the final answer to 3 decimal places.)

Value of the test statistic _______ -0.306, -0.312 Incorrect.

Please note the incorrect answers. Thank you.

Answer 1

Answer)

A)

Plan A : u1 = 58500, s1 = 8000, n1 = 38

Plan B : u2 = 59100, S2= 9500, n2= 42

Ho : u2 = u1

Ha : u2>u1

From t table, for degrees of freedom smaller of n11-, n2-1, in this case 37 and significance level of 0.02

Critical value t = 2.129

Decision rule is if t > 2.129, reject Ho.

B)

Test statistics t = (u2-u1)/sqrt(s²_p/n₁ + s²_p/n₂)

s²_p=(n₁-1* s²₁+ n₂-1* s²₂)/(n1+n2-2)

Sp^2 = 77798076.923076

t = 0.304

As the obtained t is not greater than the critical value 2.129, we fail to reject the Ho