Discuss the below:
Q1 Find the sample proportions and test statistic for equal proportions. Is the decision close? Find the p-value.
a. Dissatisfied workers in two companies: x1 = 40, n1 = 100, x2 = 30, n2 = 100, α = .05, two tailed test.
b. Rooms rented at least a week in advance at two hotels: x1 = 24, n1 = 200, x2 = 12, n2 = 50, α = .01, left-tailed test.
c. Home equity loan default rates in two banks: x1 = 36, n1 = 480, x2 = 26, n2 = 520, α = .05,
right-tailed test.
Q2 In 1999, a sample of 200 in-store shoppers showed that 42 paid by debit card. In 2004, a sample of the same size showed that 62 paid by debit card.
(a) Formulate appropriate hypotheses to test whether the percentage of debit card shoppers increased.
(b) Carry out the test at α = .01.
(c) Find the p-value.
(d) Test whether normality may be assumed
Q3 Do a two-sample test for equality of means assuming equal variances. Calculate the p-value.
a. Comparison of GPA for randomly chosen college juniors and seniors: ¯x1 = 3.05, s1 = .20, n1 = 15, ¯x2 = 3.25, s2 = .30, n2 = 15, α = .025, left-tailed test.
b. Comparison of average commute miles for randomly chosen students at two community colleges: ¯x1 = 15, s1 = 5, n1 = 22, ¯x2 = 18, s2 = 7, n2 = 19, α = .05, two-tailed test.
c. Comparison of credits at time of graduation for randomly chosen accounting and economics students: ¯x1 = 139, s1 = 2.8, n1 = 12, ¯x2 = 137, s2 = 2.7, n2 = 17, α = .05, right-tailed test.
Q4 Scrap rates per thousand (parts whose defects cannot be reworked) are compared for 5 randomly selected days at three plants. Does the data prove a significant difference in mean scrap rates?
ScrapRate
Plant A Plant B Plant C
11.4 11.1 10.2
12.5 14.1 9.5
10.1 16.8 9.0
13.8 13.2 13.3
13.7 14.6 5.9
Q5 Semester GPAs are compared for seven randomly chosen students in each class level at Oxnard University. Does the data prove a significant difference in mean GPAs? GPA1
Accounting Finance Human Resources Marketing
2.48 3.16 2.93 3.54
2.19 3.01 2.89 3.71
2.62 3.07 3.48 2.94
3.15 2.88 3.33 3.46
3.56 3.33 3.53 3.50
2.53 2.87 2.95 3.25
3.31 2.85 3.58 3.20