The accompanying TI-83/84 Plus calculator display results from thehypothesis test described in Exercise 1. Assume that the hypothesis test requirements are allsatisfied. Identify the test statistic and the P-value (expressed in standard form and rounded tothree decimal places), and then state the conclusion about the null hypothesis.

Short Answer

Expert verified

The test statistic is 64.517 and the p-value is 0.000.

The decision is to reject the null hypothesis, which implies there is insufficient evidence to conclude that the ear preference is independent of handedness.

Step by step solution

01

Given information

The hypothesis test is conducted for the data in exercise 1. It is assumed that all requirements of the test are satisfied and the results for the test are given in the accompanying image.

02

Identify the test statistic

The hypothesis for independence of ear preference and handedness is tested using chi-square test when the assumptions are satisfied.

From the provided result, the test statistic can be observed as\[{\chi ^2} = 64.5172694\].

Thus, the chi- square test statistic is 64.517.

03

Identify the P-value

P-value is the probability of getting the value as extreme as test statistic.

Thus, the associated P-value can be observed as 0.000.

04

State the decision

Assume the level of significance is 0.05.

Since the P-value (0.000) is less than the level of significance (0.05), the null hypothesis is rejected at 0.05 level of significance.

Therefore, the decision is to reject the null hypothesis.

05

State the conclusion

There is not enough evidence at 0.05 level of significance to conclude that the handedness and cell phone ear preference are independent.

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Most popular questions from this chapter

Exercises 1–5 refer to the sample data in the following table, which summarizes the last digits of the heights (cm) of 300 randomly selected subjects (from Data Set 1 “Body Data” in Appendix B). Assume that we want to use a 0.05 significance level to test the claim that the data are from a population having the property that the last digits are all equally likely.

Last Digit

0

1

2

3

4

5

6

7

8

9

Frequency

30

35

24

25

35

36

37

27

27

24

What are the null and alternative hypotheses corresponding to the stated claim?

Chocolate and Happiness Use the results from part (b) of Cumulative Review Exercise 2 to test the claim that when asked, more than 80% of women say that chocolate makes them happier. Use a 0.01 significance level.

A study of people who refused to answer survey questions provided the randomly selected sample data shown in the table below (based on data from “I Hear You Knocking But You Can’t Come In,” by Fitzgerald and Fuller, Sociological Methods and Research,Vol. 11, No. 1). At the 0.01 significance level, test the claim that the cooperation of

the subject (response or refusal) is independent of the age category. Does any particular age group appear to be particularly uncooperative?

Age


18-21

22-29

30-39

40-49

50-59

60 and over

Responded

73

255

245

136

138

202

Refused

11

20

33

16

27

49

Refer to the data given in Exercise 1 and assume that the requirements are all satisfied and we want to conduct a hypothesis test of independence using the methods of this section. Identify the null and alternative hypotheses.

Cybersecurity When using the data from Exercise 1 to test for goodness-of-fit with the distribution described by Benford’s law, identify the null and alternative hypotheses.

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