Question

# demographic markets – the Urban and Rural markets. As such, in each market, you run a...

demographic markets – the Urban and Rural markets. As such, in each market, you run a short survey that gauges customers demand for your product and assigns them to one of three categories – (i) High (ii) Medium or (iii) Low.

You survey 120 people in the “Urban” market and find that their demand falls into the following “buckets”

High 42

Medium 36

Low 42

You survey 80 people in the “Rural” market time. Their demand for the product its reflected below.

High 38

Medium 24

Low 18

The Null hypothesis that you are asked to test is that "the demand for the product is INDEPENDENT of the whether the market is Urban or Rural".

(A) Under this null hypothesis, what is the EXPECTED NUMBER OF PEOPLE THAT WILL ANSWER "HIGH" in the URBAN Market?

(B) Under this null hypothesis, what is the EXPECTED NUMBER OF PEOPLE THAT WILL ANSWER "LOW" in the RURAL Market?

(C) CALCULATE THE TEST STATISTIC FOR THE NULL HYPOTHESIS ABOVE. Enter that answer below as a number with two significant decimal places (such as 8.94 or 2.34 or 213.45)

(D) Using the critical values for the 5% and 1% levels of the Chi-Square Distribution from your text, which of the following statements is true?

 We can reject the null hypothesis at the 1% level. We can reject the null hypothesis at the 5% level. We cannot reject the null hypothesis at the 5% or 1% level We can reject the null hypothesis at both the 5% and the 1% levels.

 Column and Row Totals Urban Rural Row Totals High 42 38 80 Medium 36 24 60 Low 42 18 60 Column Totals 120 80 200  (Grand Total) Results Urban Rural Row Totals High 42  (48.00)  [0.75] 38  (32.00)  [1.12] 80 Medium 36  (36.00)  [0.00] 24  (24.00)  [0.00] 60 Low 42  (36.00)  [1.00] 18  (24.00)  [1.50] 60 Column Totals 120 80 200  (Grand Total) Numbers inside the bracket are expected values. The chi-square statistic is 4.375. The p-value is .112197. The result is not significant at p < .05

The chi-square statistic is 4.375. The p-value is .112197. The result is not significant at p < .01.

We cannot reject the null hypothesis at 5% and 1% Level of significance.

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