Math

Data were collected, using a sample survey, on the inhabitants of a British town. Among other things, the respondents were asked their age and their satisfaction with the shopping opportunities in the local high street. These data were used to construct a contingency table, with 4 age categories for its rows, and 5 categories of satisfaction for its columns. The researchers wanted to use this table to test the null hypothesis that satisfaction with the high street opportunities and age are independent. The χ² test statistic turned out to be 17.209. (You may assume that all the expected values are greater than 5.) Choose the one correct option that describes what the researchers should conclude.

Select one:
The null hypothesis is rejected at the 5% significance level, but cannot be rejected at the 1% significance level. Therefore there is little evidence that satisfaction with high street shopping is related to age.
The null hypothesis is rejected at the 1% significance level. Therefore there is little evidence that satisfaction with high street shopping is related to age.
The null hypothesis cannot be rejected at the 5% significance level. Therefore there is little evidence that satisfaction with high street shopping is related to age.
The null hypothesis is rejected at the 5% significance level, but cannot be rejected at the 1% significance level. Therefore there is moderate evidence that satisfaction with high street shopping is related to age.
The null hypothesis is rejected at the 1% significance level. Therefore there is strong evidence that satisfaction with high street shopping is related to age.
The null hypothesis cannot be rejected at the 5% significance level. Therefore there is strong evidence that satisfaction with high street shopping is related to age.

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  1. df = (4-1)(5-1) = 12

    Looking up 17.209 at 12 df gives you .20>P>.10.

    What does that tell you?

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  2. That p is greater than 0.10 so there is indeed little evidence against the hypothesis?

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