A local retailer is trying to decide where to place a new store. The retailer wo
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Question
A local retailer is trying to decide where to place a new store. The retailer wonders if working-age residents’ average wage-and-salary incomes are the same across the region. A census of local residents would be impossible.1. Give the p-value of this test if the significance level was 1%, 5%, and 10%. 2. State the statistical conclusion of each? 3. State the rejection rule using the significance levels 1%, 5%, and 10%.
National data indicate that men and women don’t have the same average income. A local employment attorney wonders whether the same is true of the working-age residents of the Metro East group’s above. A census of local residents would be impossible.
1. Test whether this is true Using the significance level of 10% 2. The firm is curious is the data has some relation to each other. (This would be a Type II error) Which significance level (1% or 10%) would reflect this curiosity? National data indicate that men and women don’t have the same average income. A local employment attorney wonders whether the same is true of the working-age residents of the Metro East group’s above. A census of local residents would be impossible.
1. Test whether this is true Using the significance level of 10% 2. The firm is curious is the data has some relation to each other. (This would be a Type II error) Which significance level (1% or 10%) would reflect this curiosity? 3. Using the significance level you chose, what did you conclude? Anova Single Factor SUMMARY Count Average Variance 790 38520770 48760.47 3.08E+09 845 24518630 29016.13 8.8E+08 Groups Sum Male Female ANOVA Df P-valueF crit Source of Variationn Between Groups MS 1.59E+11 3.18E+12 1633 1.94E+09 3.34E+12 1634 1.59E+11 81.8344 4.09E- 3.84716 19 Within Groups Total Only working age residents, ages 25-54, in the Metro East are included in the two different sex groups .Based on the United States Bureau of the Census, American Community Survey 2015 for Illinois. Restricted to four residents PUMAs in the Metro East: 1104 (St. Clair Northeast) 1105 (St. Clair South & West), 1204 (Madison East), and 1205 (Madison West). (https://www.census.gov/gco/maps-data/maps/201Opuma/st17 il.htm Last updated October 3, 2016. Accessed May 12, 2017
Explanation / Answer
A local retailer is trying to decide where to place a new store. The retailer wonders if working-age residents’ average wage-and-salary incomes are the same across the region. A census of local residents would be impossible.
1) P-value of this test at 5% is < 0.00001. The result is significant at p < .05.
P value of this test at 1% is < 0.00001. The result is significant at p < .01.
P-value of this test at 10% is < .00001. The result is significant at p < .10
2) Statistical Conclusion at 1% level of Significance is REJECT NULL Hypothesis H0.
Statistical Conclusion at 5% level of Significance is REJECT NULL Hypothesis H0.
Statistical Conclusion at 10% level of significance is REJECT NULL HYPOTHESIS H0.
3) Rejection rule at 1%: If p value <0.01 , it is significant then reject null hypothesis H0 at 1% level of significance. If P-value > 0.01 it is not significant then DO NOT REJECT NULL HYPOTHESIS H0.
Rejection rule at 5% : If p value<0.05, it is significant, then REJECT NULL HYPOTHESIS H0. If p value> 0.05 it is NOT significant then DO NOT REJECT NULL HYPOTHESIS H0.
Rejection rule 10% : If P-value < 0.1 , it is significant then REJECT NULL HYPOTHESIS H0 . If P-value> 0.1 then it is NOT significant then DO NOT REJECT NULL HYPOTHESIS H0.
National data indicate that men and women don’t have the same average income. A local employment attorney wonders whether the same is true of the working-age residents of the Metro East group’s above. A census of local residents would be impossible.
1) For F statistic 81.83 with (1,1633) df the p-value is < .00001. The result is significant at p < .10.
Hence we reject Null hypothesis H0 at 10% level of significance and conclude that men and women don’t have the same average income.
2) Since p value is very small and 10% level of significance large as compared to 1%. So to avoid Type II error, firm will select 1% level of Significance.
3) For F stat 81.83 with (1,1633) d.f the P-value is <0.00001 which is again significant at p<.01
Therefore we conclude that the men and women don’t have the same average income.
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