15.7. CHAPTER 15 EXERCISES 401 It has recently been hypothesized by a mathematic

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15.7. CHAPTER 15 EXERCISES 401 It has recently been hypothesized by a mathematics professor that in the United States, a person's ideology and heir opinion on the war against terrorism are in fact related. To test this hypothesis, the professor randomly contacted 600 individuals in the United States and recorded each person's ideological position, as well as their opinion concerning the war on terrorism. The data is given in the table below. Does the sample data suggest that, for people in the United States, ideology and opinion concerning the war on terrorism are related? Justified Not Justified Liberal Moderate Conservative 94 188 162 106 12 15. After playing a game of chance with a friend that involved rolling a single die, you suspect that the die that was used, which was supplied by your friend, was not fair. You contact your friend and manage to get the die that was used. After rolling the die 600 times, you collect the data given in the table below. Does the data suggest that the die used in the game was fair? Face Value 12 T34 56 | Frequency-301 126188-2 102 82 The use of cellular phones while driving has become an issue in many states recently. The question that needs o be addressed is whether a person driving is more likely to be involved in an accident when they are using a cellular phone. Does the data given in the table below suggest that a person using a cellular phone is in fact more likely to be involved in an accident? Use TWO DIFFERENT techniques to analyze this data and

Explanation / Answer

Question 15

Here we will check that dice is fair or not.

so hypothesis are

H0 : The dice is fair one. pi = 1/6

Ha : The dice is not fair one. pi 1/6

so there are 600 trials.

So expected number of 1's, 2's....= 600/6 = 100

so the observed and expected table.

so X2 = 28.32

here degree of freedom dF = 6 -1 = 5 and significance level = 0.05

so X2critical  = X20.05,5 = 11.0705

We can conclude that the dice is not fair.

so X2 > X2criical so we shall reject the null hypothesis.

Roll Observed(O) Expected (E) (O -E) (O - E)^2 (O - E)^2/E 1 130 100 30 900 9 2 126 100 26 676 6.76 3 88 100 -12 144 1.44 4 72 100 -28 784 7.84 5 102 100 2 4 0.04 6 82 100 -18 324 3.24 Sum 28.32

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