Question

1) A college believes that 24% of applicants to that school have parents who have remarried. How large a sample is needed to estimate the true proportion of students who have parents who have remarried to within 3 percentage points with 99% confidence?

2) Using Table G, find the values for chi square left and right  for α = .10 and n = 12.

3) In a study of 50 new cars, 20 of them were white. Find p^ and q^ where p^  where is the proportion of new cars that is white.

4) In a particular city, the average salary of secretaries is $31000 per year. Secretaries at Company A claim that they are paid less than the city average. In a sample of 55 secretaries, their average salary was $27000 per year with a standard deviation of $4000. What is the test value for this hypothesis?

5)) When conducting a two-tailed z -test with α = 0.01, the test value was 2.07. The decision would be: do not reject the null hypothesis. TRUE OR FALSE

Answer 1

1)

Sample size, n =

z value for 99% confidence level is 2.576

Margin of Error, E = 3/100 = 0.03

Sample size, n =

= 1345 (Rounded to nearest integer)

2)

Degree of freedom = n -1 = 12 - 1 = 11

Chi square left value at df = 12 and α = .10 is  4.5748

Chi square right value at df = 12 and α = .10 is  19.6751

3)

p^ = 20 / 50 = 0.4

q^ = 1 - p^ = 1 - 0.4 = 0.6

4)

Standard error of mean = 4000 / = 539.36

Test statistic = (27000 - 31000) / 539.36 = -7.42

5)

Critical value of z statistic at α = 0.01 for two-tailed test is 2.576

Since the test value is less than the critical value, decision would be: do not reject the null hypothesis

The statement is TRUE.