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Do the data provide convincing evidence of a difference in the effectiveness of the four treatments? Carry out an appropriate test at the =0.05significance level.

Short Answer

Expert verified

Yes, there is sufficient evidence that there is an association between the variables.

Step by step solution

01

Given information

The given data is

02

Explanation

Observed counts

The expected counts are the row total multiplied by the column total, divided by the sample sizen=6602

The chi-square statistic is the sum of squared deviations (between observed and expected counts) divided by the expected count:

localid="1650644880819" 2=(250-205.8128)2205.8128+(206-205.8128)2205.8128+(211-206.4368)2206.4368+(157-205.9376)2205.9376+(1399-1443.1872)21443.1872+(1443-1443.1872)21443.1872+(1443-1447.5632)21447.5632+(1493-1444.0624)21444.0624=24.243

The interval for the P-value can then be found in table C in the column title which have the X2-value in the corresponding interval in the row with

localid="1650644859112" df=(c-1)(r-1)=(4-1)(2-1)=3

The two tailed pvalue is 0.000044

P<0.0005

If the P-value is smaller than the significance level, then the null hypothesis is rejected.

P<0.05RejectH0

There is sufficient evidence that there is an association between the variables.

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