To test whether the proportion of people living in the different regions changed between Year A and Year B, we can conduct a chi-square test of independence.
The null hypothesis is that the proportion of people living in the different regions is the same between Year A and Year B.
The alternative hypothesis is that the proportion of people living in the different regions is not the same between Year A and Year B.
To calculate the p-value, we need to first calculate the expected frequencies under the null hypothesis. We can do this by multiplying the total sample size (1000) by the proportion of people living in each region in Year A.
Expected frequencies:
Northeast: 0.181 * 1000 = 181
Midwest: 0.248 * 1000 = 248
South: 0.343 * 1000 = 343
West: 0.228 * 1000 = 228
Next, we calculate the chi-square statistic using the formula:
X^2 = Σ((O-E)^2 / E)
where O is the observed frequency and E is the expected frequency.
Calculating the chi-square statistic:
((152-181)^2 / 181) + ((227-248)^2 / 248) + ((390-343)^2 / 343) + ((231-228)^2 / 228) = 11.49
To find the p-value, we look up the chi-square value of 11.49 with 3 degrees of freedom (4 regions - 1) in a chi-square table. The critical chi-square value at α = 0.05 with 3 degrees of freedom is approximately 7.815.
Since 11.49 is greater than 7.815, we reject the null hypothesis. This means that we have sufficient evidence to conclude that the proportion of people living in the different regions changed between Year A and Year B.
The US census bureau computed the proportion of US residents who lived in each of 4 geographic regions in Year A. Then a simple random sample was drawn of 1000 people living in the US in year b. The following data is the results. Northeast: Year A :0.181, Year B: 152; Midwest: year a : 0.248, year b :227; South Year A: 0.343, year b 390; West: year a: 0.228, year b: 231;
Can you conclude that the proportion of people living in the various regions changed between year a and year b. Use the a= 0.05 level of significance. First find the P- value
3 answers
Find the P- value and round to 4 Decimal places
To find the p-value associated with the chi-square statistic of 11.49 with 3 degrees of freedom, we can use a chi-square distribution table or a statistical software.
Using a statistical software or calculator, the p-value corresponding to a chi-square statistic of 11.49 with 3 degrees of freedom is approximately 0.0099.
Therefore, the p-value, rounded to 4 decimal places, is 0.0099.
Using a statistical software or calculator, the p-value corresponding to a chi-square statistic of 11.49 with 3 degrees of freedom is approximately 0.0099.
Therefore, the p-value, rounded to 4 decimal places, is 0.0099.
33 answers