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# Two Sample T test for testing the Hypothesis of Means

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An experiment was conducted to compare mean reaction time to 2 types of traffic signs, prohibitive (No Left Turn) and permissive (Left Turn Only). Ten subjects were included in the experiment. Each subject was presented with 40traffice signs: 10 prohibitive and 10 permissive in random order. The mean time to reaction and the number of correct actions were recorded for each subject. The mean reaction times to both are listed below:

Table Mean Reaction Times for 20 Traffic Signs
Prohibitive Permissive
1 824 737
2 866 585
3 841 718
4 770 723
5 829 675
6 764 711
7 857 626
8 831 697
9 846 730
10 759 739

a. Explain why or why not this study is a paired-difference design. Provide reasons why pairing or independent samples should be useful in increasing information regarding the difference between the mean reaction times to prohibitive and permissive traffic signs.

b. Determine if the there is sufficient evidence to indicate a difference in the mean reaction times of prohibitive and permissive traffic signs.

1. What are the null and alternative hypotheses?

2. What is the level of significance?

3. Test the null hypothesis, what can you conclude? (Be sure to include the test statistic, critical value, p-value and an interpretive statement)

4. What are 2 plausible alternative explanations for the results?

5. What are the implications of the results (include a course of action)?

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## Question from Applied Statistics in Business and Economics by Doane and Seward. Chapter 10: Numbers 10.2, 10.3, and 10.13 Chapter 11: Numbers 11.1 and 11.3

10.2 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, &#945; = .05, two tailed
test.

b. Rooms rented at least a week in advance at two hotels: x1 = 24, n1 = 200, x2 = 12, n2 = 50,
&#945; = .01, left-tailed test.

c. Home equity loan default rates in two banks: x1 = 36, n1 = 480, x2 = 26, n2 = 520, &#945; = .05,
right-tailed test.

10.3 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 &#945; = .01.

(c) Find the p-value.

(d) Test whether normality may be assumed

10.13 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, &#945; = .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, &#945; = .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, &#945; = .05, right-tailed test.

11.1 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

11.3 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

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