Random samples of people ages 15−24 and of people ages 25−34 were asked about their preferred method of (remote) communication with friends. The respondents were asked to select one of the methods from the following list: cell phone, instant message, e-mail, other. Preferred Communication Method Age Cell Phone Instant Message Email Other Row Total 15-24 39 45 7 9 100 25-34 46 27 13 14 100 Column Total 85 72 20 23 200 ( (ii) Test whether the two populations share the same proportions of preferences for each type of communication method. Use α = 0.05. (b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Random samples of people ages 15−24 and of people ages 25−34 were asked about their preferred method of (remote) communication with friends. The respondents were asked to select one of the methods from the following list: cell phone, instant message, e-mail, other.
| Preferred Communication Method | |||||
| Age | Cell Phone | Instant Message | Other | Row Total | |
| 15-24 | 39 | 45 | 7 | 9 | 100 |
| 25-34 | 46 | 27 | 13 | 14 | 100 |
| Column Total | 85 | 72 | 20 | 23 | 200 |
(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)
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