In Example 2 we found that there was not enough evidence to support the conclusion that the distribution of the population in the United States was shifting. The following table shows the results of a survey of n = 5000 households.

Region                                     Frequency
Northeast ................................       900
Midwest ...................................    1089
South ........................................    1846
West .........................................    1165

(a) Refer to the distribution of households in 2000 from Example 2. Determine the expected number of households in each region under the assumption the population distribution has not changed since 2000.

(b) Determine the proportion of households in each region based on the results of the survey. Compare these proportions to those in Table 2 from Example 2. What do you notice?

(c) Does the sample evidence above suggest that the distribution of residents in the United States has changed since 2000?

(d) Discuss the role sample size can play in determining whether the statement in the null hypothesis is rejected.