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After randomly assigning subjects to treatments in a randomized comparative experiment, we can compare the treatment groups to see how well the random assignment worked. We hope to find no significant differences among the groups. A study on how to provide premature infants with a substance essential to their development assigned infants at random to receive one of four types of supplements, called PBM, NLCP, PL-LCP, and TG-LCP. The subjects were 77premature infants. In the experiment, 20were assigned to the PBM group and 19to each of the other treatments.

(a) The random assignment resulted in 9females in the TG-LCP group and 11 females in each of the other groups. Make a two-way table of the group by gender. Calculate the proportion of females in each treatment group. Does it appear that the random assignment roughly balanced the groups by gender? Explain.

(b) Are the differences between the groups statistically significant? Give appropriate evidence to support your answer.

Short Answer

Expert verified

(a) No, it does not appear that the random assignment roughly balanced the groups by gender.

(b) No, the differences between the groups are not statistically significant.

Step by step solution

01

Part (a) Step 1: Given information

Number of premature infants is 77

PGM group is 20

Other treatments is19

02

Part (a) Step 2: Explanation

The number of males is the number in the group decreased by the number of females

The proportions in each group is the number of infants divided by the row total given in the last column:

The proportions appears to be balanced, because there are no large differences between the proportions.

03

Part (b) Step 1: Given information

The number of premature infants is 77

PGM group is 20

Other treatments is19

04

Part (b) Step 2: Explanation

Observed counts

The expected counts are the row total multiplied by the column total, divided by the sample sizen=77

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

localid="1650644257312" 2=(9-9.0909)29.0909+(8-8.6364)28.6364+(8-8.6364)28.6364+(10-8.6364)28.6364+(11-10.9091)210.9091+(11-10.3636)210.3636+(11-10.3636)210.3636+(9-10.3636)210.3636=0.5683

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

localid="1650644276147" df=(c-1)(r-1)=(4-1)(2-1)=3

localid="1650644291222" p>0.25

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

P>0.05FailtorejectH0

There is not sufficient evidence that there is an association between the variables.

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Most popular questions from this chapter

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Aw, nuts! Calculate the chi-square statistic for the data in Exercise 1. Show your work.

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