Question

A drug company is developing a product which is intended to shorten the duration of colds....

A drug company is developing a product which is intended to shorten the duration of colds. To determine if the product is effective, a study is done with two groups of physiologically similar people. The placebo group is given a sugar pill, the treatment group is given the cold remedy, and the results are given below.

 Cold duration (days) Placebo group (relative frequency) Treatment group (frequency) 0-5 days 40% 102 6-9 days 35% 70 10-12 days 15% 14 13+ days 10% 14

We want to determine whether or not there is a significant difference in the distribution of the cold durations between the placebo group and the treatment group. Use α = .01 to make your conclusion.

The value of the chi-square statistic is:

The p-value of the test is:

applying chi square test:

 relative observed Expected residual Chi square category frequency Oi Ei=total*p R2i=(Oi-Ei)/√Ei R2i=(Oi-Ei)2/Ei 1 0.400 102 80.00 2.46 6.050 2 0.350 70 70.00 0.00 0.000 3 0.150 14 30.00 -2.92 8.533 4 0.100 14 20.00 -1.34 1.800 total 1.000 200 200 16.383

value of the chi-square statistic =16.3833

p-value of the test is =0.0009

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